Fast folding algorithm - Revision history

Comp.arch at 10:29, 16 December 2024

2024-12-16T10:29:40Z

← Previous revision		Revision as of 10:29, 16 December 2024
Line 1:		Line 1:
		⚫	The '''Fast-Folding Algorithm''' (FFA) is a computational method primarily utilized in the domain of astronomy for detecting periodic signals.<ref name=":0">{{Cite journal \|last1=Parent \|first1=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357\|doi-access=free \|arxiv=1805.08247 \|bibcode=2018ApJ...861...44P }}</ref>
	The '''Fast-Folding Algorithm''' (FFA) is a computational method primarily utilized in the domain of astronomy for detecting periodic signals.
⚫	<ref name=":0">{{Cite journal \|last1=Parent \|first1=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357\|doi-access=free \|arxiv=1805.08247 \|bibcode=2018ApJ...861...44P }}</ref>
	FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":0" />		FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":0" />
	A quintessential application of FFA is in the detection and analysis of [[pulsar]]s—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />		A quintessential application of FFA is in the detection and analysis of [[pulsar]]s—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />

	== History of the FFA ==		== History of the FFA ==
	The Fast Folding Algorithm (FFA) has its roots dating back to 1969 when it was introduced by Professor [[David H. Staelin]] from the [[Massachusetts Institute of Technology\|Massachusetts Institute of Technology (MIT)]].		The Fast Folding Algorithm (FFA) has its roots dating back to 1969 when it was introduced by Professor [[David H. Staelin]] from the [[Massachusetts Institute of Technology\|Massachusetts Institute of Technology (MIT)]].<ref name=":1">{{Citation \| last=Staelin \| first=David H. \| title=Fast Folding Algorithm for Detection of Periodic Pulse Trains \| journal=Proceedings of the IEEE \| volume=57 \| issue=4 \| pages=724–5 \| date=1969 \|doi=10.1109/PROC.1969.7051\| bibcode=1969IEEEP..57..724S }}</ref>
	<ref name=":1">{{Citation \| last=Staelin \| first=David H. \| title=Fast Folding Algorithm for Detection of Periodic Pulse Trains \| journal=Proceedings of the IEEE \| volume=57 \| issue=4 \| pages=724–5 \| date=1969 \|doi=10.1109/PROC.1969.7051\| bibcode=1969IEEEP..57..724S }}</ref>
	At the time, the scientific community was deeply involved in the study of pulsars, which are rapidly rotating [[neutron star]]s emitting beams of electromagnetic radiation. Professor Staelin recognized the potential of the FFA as a powerful instrument for detecting periodic signals within these pulsar surveys. These surveys were not just about understanding pulsars but held a much broader significance. They played a pivotal role in testing and validating Einstein's [[General relativity\|theory of general relativity]], a cornerstone in the field of [[Astronomy]]. As the years progressed, the FFA saw various refinements, with researchers making tweaks and optimizations to enhance its efficiency and accuracy. Despite its potential, the FFA was mostly underutilized thanks to the dominance of [[Fast Fourier transform\|Fast Fourier Transform (FFT)]]-based techniques, which were the preferred choice for many in [[signal processing]] during that era. As a result, while the FFA showed promise, its applications in the broader scientific community remained underutilized for several decades.<ref name=":0" />		At the time, the scientific community was deeply involved in the study of pulsars, which are rapidly rotating [[neutron star]]s emitting beams of electromagnetic radiation. Professor Staelin recognized the potential of the FFA as a powerful instrument for detecting periodic signals within these pulsar surveys. These surveys were not just about understanding pulsars but held a much broader significance. They played a pivotal role in testing and validating Einstein's [[General relativity\|theory of general relativity]], a cornerstone in the field of [[Astronomy]]. As the years progressed, the FFA saw various refinements, with researchers making tweaks and optimizations to enhance its efficiency and accuracy. Despite its potential, the FFA was mostly underutilized thanks to the dominance of [[Fast Fourier transform\|Fast Fourier Transform (FFT)]]-based techniques, which were the preferred choice for many in [[signal processing]] during that era. As a result, while the FFA showed promise, its applications in the broader scientific community remained underutilized for several decades.<ref name=":0" />

12.151.182.195: /* Technical Foundations of the FFA[edit] */ Remove leftover [EDIT] tag that shouldn't have been in the title

2024-09-20T19:11:06Z

Technical Foundations of the FFA[edit]: Remove leftover [EDIT] tag that shouldn't have been in the title

← Previous revision		Revision as of 19:11, 20 September 2024
Line 9:		Line 9:
	At the time, the scientific community was deeply involved in the study of pulsars, which are rapidly rotating [[neutron star]]s emitting beams of electromagnetic radiation. Professor Staelin recognized the potential of the FFA as a powerful instrument for detecting periodic signals within these pulsar surveys. These surveys were not just about understanding pulsars but held a much broader significance. They played a pivotal role in testing and validating Einstein's [[General relativity\|theory of general relativity]], a cornerstone in the field of [[Astronomy]]. As the years progressed, the FFA saw various refinements, with researchers making tweaks and optimizations to enhance its efficiency and accuracy. Despite its potential, the FFA was mostly underutilized thanks to the dominance of [[Fast Fourier transform\|Fast Fourier Transform (FFT)]]-based techniques, which were the preferred choice for many in [[signal processing]] during that era. As a result, while the FFA showed promise, its applications in the broader scientific community remained underutilized for several decades.<ref name=":0" />		At the time, the scientific community was deeply involved in the study of pulsars, which are rapidly rotating [[neutron star]]s emitting beams of electromagnetic radiation. Professor Staelin recognized the potential of the FFA as a powerful instrument for detecting periodic signals within these pulsar surveys. These surveys were not just about understanding pulsars but held a much broader significance. They played a pivotal role in testing and validating Einstein's [[General relativity\|theory of general relativity]], a cornerstone in the field of [[Astronomy]]. As the years progressed, the FFA saw various refinements, with researchers making tweaks and optimizations to enhance its efficiency and accuracy. Despite its potential, the FFA was mostly underutilized thanks to the dominance of [[Fast Fourier transform\|Fast Fourier Transform (FFT)]]-based techniques, which were the preferred choice for many in [[signal processing]] during that era. As a result, while the FFA showed promise, its applications in the broader scientific community remained underutilized for several decades.<ref name=":0" />

	== Technical Foundations of the FFA~~[edit]~~ ==		== Technical Foundations of the FFA ==
	The Fast Folding Algorithm (FFA) was initially developed as a method to search for periodic signals amidst noise in the [[time domain]], contrasting with the FFT search technique that operates in the [[frequency domain]]. The primary advantage of the FFA is its efficiency in avoiding redundant summations (unnecessary additional computations). Specifically, the FFA is much faster than standard folding at all possible trial periods, achieving this by performing summations through N×log2(N/p−1) steps rather than N×(N/p−1). This efficiency arises because the logarithmic term log2(N/p−1) grows much slower than the linear term (N/p−1), making the number of steps more manageable as N increases, N represents the number of samples in the [[time series]], and p is the trial folding period in units of samples. The FFA method involves folding each time series at multiple periods, performing partial summations in a series of log2(p) stages, and combining those sums to fold the data with a trial period between p and p+1. This approach retains all harmonic structures, making it especially effective for identifying narrow-pulsed signals in the long-period regime. One of the FFA's unique features is its hierarchical approach to folding, breaking the data down into smaller chunks, folding these chunks, and then combining them. This method, combined with its inherent tolerance to noise and adaptability for different types of data and hardware configurations, ensures the FFA remains a powerful tool for detecting periodic signals, especially in environments with significant noise or interference which makes it especially useful for Astronomical endavours.<ref name=":0" />{{Short description\|Method for detecting periodic signals}}		The Fast Folding Algorithm (FFA) was initially developed as a method to search for periodic signals amidst noise in the [[time domain]], contrasting with the FFT search technique that operates in the [[frequency domain]]. The primary advantage of the FFA is its efficiency in avoiding redundant summations (unnecessary additional computations). Specifically, the FFA is much faster than standard folding at all possible trial periods, achieving this by performing summations through N×log2(N/p−1) steps rather than N×(N/p−1). This efficiency arises because the logarithmic term log2(N/p−1) grows much slower than the linear term (N/p−1), making the number of steps more manageable as N increases, N represents the number of samples in the [[time series]], and p is the trial folding period in units of samples. The FFA method involves folding each time series at multiple periods, performing partial summations in a series of log2(p) stages, and combining those sums to fold the data with a trial period between p and p+1. This approach retains all harmonic structures, making it especially effective for identifying narrow-pulsed signals in the long-period regime. One of the FFA's unique features is its hierarchical approach to folding, breaking the data down into smaller chunks, folding these chunks, and then combining them. This method, combined with its inherent tolerance to noise and adaptability for different types of data and hardware configurations, ensures the FFA remains a powerful tool for detecting periodic signals, especially in environments with significant noise or interference which makes it especially useful for Astronomical endavours.<ref name=":0" />{{Short description\|Method for detecting periodic signals}}
	In [[signal processing]], the '''fast folding algorithm'''<ref name=":1" /> is an efficient [[algorithm]] for the detection of approximately-[[periodic function\|periodic]] events within [[time series]] data. It computes superpositions of the signal modulo various window sizes simultaneously.		In [[signal processing]], the '''fast folding algorithm'''<ref name=":1" /> is an efficient [[algorithm]] for the detection of approximately-[[periodic function\|periodic]] events within [[time series]] data. It computes superpositions of the signal modulo various window sizes simultaneously.

12.151.182.195: /* History of the FFA[edit] */ Remove leftover [EDIT] tag that shouldn't have been in the title

2024-09-20T19:10:47Z

History of the FFA[edit]: Remove leftover [EDIT] tag that shouldn't have been in the title

← Previous revision		Revision as of 19:10, 20 September 2024
Line 4:		Line 4:
	A quintessential application of FFA is in the detection and analysis of [[pulsar]]s—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />		A quintessential application of FFA is in the detection and analysis of [[pulsar]]s—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />

	== History of the FFA~~[edit]~~ ==		== History of the FFA ==
	The Fast Folding Algorithm (FFA) has its roots dating back to 1969 when it was introduced by Professor [[David H. Staelin]] from the [[Massachusetts Institute of Technology\|Massachusetts Institute of Technology (MIT)]].		The Fast Folding Algorithm (FFA) has its roots dating back to 1969 when it was introduced by Professor [[David H. Staelin]] from the [[Massachusetts Institute of Technology\|Massachusetts Institute of Technology (MIT)]].
	<ref name=":1">{{Citation \| last=Staelin \| first=David H. \| title=Fast Folding Algorithm for Detection of Periodic Pulse Trains \| journal=Proceedings of the IEEE \| volume=57 \| issue=4 \| pages=724–5 \| date=1969 \|doi=10.1109/PROC.1969.7051\| bibcode=1969IEEEP..57..724S }}</ref>		<ref name=":1">{{Citation \| last=Staelin \| first=David H. \| title=Fast Folding Algorithm for Detection of Periodic Pulse Trains \| journal=Proceedings of the IEEE \| volume=57 \| issue=4 \| pages=724–5 \| date=1969 \|doi=10.1109/PROC.1969.7051\| bibcode=1969IEEEP..57..724S }}</ref>

Citation bot: Add: bibcode, authors 1-1. Removed URL that duplicated identifier. Removed parameters. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by Dominic3203 | [[Category:Signal processing] | #UCB_Category 83/293

2024-05-19T04:42:50Z

Add: bibcode, authors 1-1. Removed URL that duplicated identifier. Removed parameters. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by Dominic3203 | [[Category:Signal processing] | #UCB_Category 83/293

← Previous revision		Revision as of 04:42, 19 May 2024
Line 1:		Line 1:
	The '''Fast-Folding Algorithm''' (FFA) is a computational method primarily utilized in the domain of astronomy for detecting periodic signals.		The '''Fast-Folding Algorithm''' (FFA) is a computational method primarily utilized in the domain of astronomy for detecting periodic signals.
	<ref name=":0">{{Cite journal \|~~last~~=Parent \|~~first~~=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey ~~\|url=http://dx.doi.org/10.3847/1538-4357/aac5f0~~ \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357\|doi-access=free \|arxiv=1805.08247 }}</ref>		<ref name=":0">{{Cite journal \|last1=Parent \|first1=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357\|doi-access=free \|arxiv=1805.08247 \|bibcode=2018ApJ...861...44P }}</ref>
	FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":0" />		FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":0" />
	A quintessential application of FFA is in the detection and analysis of [[pulsar]]s—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />		A quintessential application of FFA is in the detection and analysis of [[pulsar]]s—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />

OAbot: Open access bot: arxiv updated in citation with #oabot.

2024-01-05T12:37:55Z

Open access bot: arxiv updated in citation with #oabot.

← Previous revision		Revision as of 12:37, 5 January 2024
Line 1:		Line 1:
	The '''Fast-Folding Algorithm''' (FFA) is a computational method primarily utilized in the domain of astronomy for detecting periodic signals.		The '''Fast-Folding Algorithm''' (FFA) is a computational method primarily utilized in the domain of astronomy for detecting periodic signals.
	<ref name=":0">{{Cite journal \|last=Parent \|first=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|url=http://dx.doi.org/10.3847/1538-4357/aac5f0 \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357\|doi-access=free }}</ref>		<ref name=":0">{{Cite journal \|last=Parent \|first=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|url=http://dx.doi.org/10.3847/1538-4357/aac5f0 \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357\|doi-access=free \|arxiv=1805.08247 }}</ref>
	FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":0" />		FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":0" />
	A quintessential application of FFA is in the detection and analysis of [[pulsar]]s—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />		A quintessential application of FFA is in the detection and analysis of [[pulsar]]s—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />

BD2412: clean up spacing around commas and other punctuation fixes, replaced: ,N → , N

2023-12-24T03:36:04Z

clean up spacing around commas and other punctuation fixes, replaced: ,N → , N

← Previous revision		Revision as of 03:36, 24 December 2023
Line 2:		Line 2:
	<ref name=":0">{{Cite journal \|last=Parent \|first=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|url=http://dx.doi.org/10.3847/1538-4357/aac5f0 \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357\|doi-access=free }}</ref>		<ref name=":0">{{Cite journal \|last=Parent \|first=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|url=http://dx.doi.org/10.3847/1538-4357/aac5f0 \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357\|doi-access=free }}</ref>
	FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":0" />		FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":0" />
	A quintessential application of FFA is in the detection and analysis of [[~~Pulsar\|pulsars~~]]~~—highly~~ magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />		A quintessential application of FFA is in the detection and analysis of [[pulsar]]s—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />

	== History of the FFA[edit] ==		== History of the FFA[edit] ==
	The Fast Folding Algorithm (FFA) has its roots dating back to 1969 when it was introduced by Professor [[David H. Staelin]] from the [[Massachusetts Institute of Technology\|Massachusetts Institute of Technology (MIT)]].		The Fast Folding Algorithm (FFA) has its roots dating back to 1969 when it was introduced by Professor [[David H. Staelin]] from the [[Massachusetts Institute of Technology\|Massachusetts Institute of Technology (MIT)]].
	<ref name=":1">{{Citation \| last=Staelin \| first=David H. \| title=Fast Folding Algorithm for Detection of Periodic Pulse Trains \| journal=Proceedings of the IEEE \| volume=57 \| issue=4 \| pages=724–5 \| date=1969 \|doi=10.1109/PROC.1969.7051\| bibcode=1969IEEEP..57..724S }}</ref>		<ref name=":1">{{Citation \| last=Staelin \| first=David H. \| title=Fast Folding Algorithm for Detection of Periodic Pulse Trains \| journal=Proceedings of the IEEE \| volume=57 \| issue=4 \| pages=724–5 \| date=1969 \|doi=10.1109/PROC.1969.7051\| bibcode=1969IEEEP..57..724S }}</ref>
	At the time, the scientific community was deeply involved in the study of pulsars, which are rapidly rotating [[~~Neutron~~ star~~\|neutron stars~~]] emitting beams of electromagnetic radiation. Professor Staelin recognized the potential of the FFA as a powerful instrument for detecting periodic signals within these pulsar surveys. These surveys were not just about understanding pulsars but held a much broader significance. They played a pivotal role in testing and validating Einstein's [[General relativity\|theory of general relativity]], a cornerstone in the field of [[Astronomy]]. As the years progressed, the FFA saw various refinements, with researchers making tweaks and optimizations to enhance its efficiency and accuracy. Despite its potential, the FFA was mostly underutilized thanks to the dominance of [[Fast Fourier transform\|Fast Fourier Transform (FFT)]]-based techniques, which were the preferred choice for many in [[signal processing]] during that era. As a result, while the FFA showed promise, its applications in the broader scientific community remained underutilized for several decades.<ref name=":0" />		At the time, the scientific community was deeply involved in the study of pulsars, which are rapidly rotating [[neutron star]]s emitting beams of electromagnetic radiation. Professor Staelin recognized the potential of the FFA as a powerful instrument for detecting periodic signals within these pulsar surveys. These surveys were not just about understanding pulsars but held a much broader significance. They played a pivotal role in testing and validating Einstein's [[General relativity\|theory of general relativity]], a cornerstone in the field of [[Astronomy]]. As the years progressed, the FFA saw various refinements, with researchers making tweaks and optimizations to enhance its efficiency and accuracy. Despite its potential, the FFA was mostly underutilized thanks to the dominance of [[Fast Fourier transform\|Fast Fourier Transform (FFT)]]-based techniques, which were the preferred choice for many in [[signal processing]] during that era. As a result, while the FFA showed promise, its applications in the broader scientific community remained underutilized for several decades.<ref name=":0" />

	== Technical Foundations of the FFA[edit] ==		== Technical Foundations of the FFA[edit] ==
	The Fast Folding Algorithm (FFA) was initially developed as a method to search for periodic signals amidst noise in the [[time domain]], contrasting with the FFT search technique that operates in the [[frequency domain]]. The primary advantage of the FFA is its efficiency in avoiding redundant summations (unnecessary additional computations). Specifically, the FFA is much faster than standard folding at all possible trial periods, achieving this by performing summations through N×log2(N/p−1) steps rather than N×(N/p−1). This efficiency arises because the logarithmic term log2(N/p−1) grows much slower than the linear term (N/p−1), making the number of steps more manageable as N increases,N represents the number of samples in the [[time series]], and p is the trial folding period in units of samples. The FFA method involves folding each time series at multiple periods, performing partial summations in a series of log2(p) stages, and combining those sums to fold the data with a trial period between p and p+1. This approach retains all harmonic structures, making it especially effective for identifying narrow-pulsed signals in the long-period regime. One of the FFA's unique features is its hierarchical approach to folding, breaking the data down into smaller chunks, folding these chunks, and then combining them. This method, combined with its inherent tolerance to noise and adaptability for different types of data and hardware configurations, ensures the FFA remains a powerful tool for detecting periodic signals, especially in environments with significant noise or interference which makes it especially useful for Astronomical endavours.<ref name=":0" />{{Short description\|Method for detecting periodic signals}}		The Fast Folding Algorithm (FFA) was initially developed as a method to search for periodic signals amidst noise in the [[time domain]], contrasting with the FFT search technique that operates in the [[frequency domain]]. The primary advantage of the FFA is its efficiency in avoiding redundant summations (unnecessary additional computations). Specifically, the FFA is much faster than standard folding at all possible trial periods, achieving this by performing summations through N×log2(N/p−1) steps rather than N×(N/p−1). This efficiency arises because the logarithmic term log2(N/p−1) grows much slower than the linear term (N/p−1), making the number of steps more manageable as N increases, N represents the number of samples in the [[time series]], and p is the trial folding period in units of samples. The FFA method involves folding each time series at multiple periods, performing partial summations in a series of log2(p) stages, and combining those sums to fold the data with a trial period between p and p+1. This approach retains all harmonic structures, making it especially effective for identifying narrow-pulsed signals in the long-period regime. One of the FFA's unique features is its hierarchical approach to folding, breaking the data down into smaller chunks, folding these chunks, and then combining them. This method, combined with its inherent tolerance to noise and adaptability for different types of data and hardware configurations, ensures the FFA remains a powerful tool for detecting periodic signals, especially in environments with significant noise or interference which makes it especially useful for Astronomical endavours.<ref name=":0" />{{Short description\|Method for detecting periodic signals}}
	In [[signal processing]], the '''fast folding algorithm'''<ref name=":1" /> is an efficient [[algorithm]] for the detection of approximately-[[periodic function\|periodic]] events within [[time series]] data. It computes superpositions of the signal modulo various window sizes simultaneously.		In [[signal processing]], the '''fast folding algorithm'''<ref name=":1" /> is an efficient [[algorithm]] for the detection of approximately-[[periodic function\|periodic]] events within [[time series]] data. It computes superpositions of the signal modulo various window sizes simultaneously.

OAbot: Open access bot: doi updated in citation with #oabot.

2023-11-27T20:37:20Z

Open access bot: doi updated in citation with #oabot.

← Previous revision		Revision as of 20:37, 27 November 2023
Line 1:		Line 1:
	The '''Fast-Folding Algorithm''' (FFA) is a computational method primarily utilized in the domain of astronomy for detecting periodic signals.		The '''Fast-Folding Algorithm''' (FFA) is a computational method primarily utilized in the domain of astronomy for detecting periodic signals.
	<ref name=":0">{{Cite journal \|last=Parent \|first=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|url=http://dx.doi.org/10.3847/1538-4357/aac5f0 \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357}}</ref>		<ref name=":0">{{Cite journal \|last=Parent \|first=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|url=http://dx.doi.org/10.3847/1538-4357/aac5f0 \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357\|doi-access=free }}</ref>
	FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":0" />		FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":0" />
	A quintessential application of FFA is in the detection and analysis of [[Pulsar\|pulsars]]—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />		A quintessential application of FFA is in the detection and analysis of [[Pulsar\|pulsars]]—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />

Phil074: fixed spacing.

2023-11-24T15:42:38Z

fixed spacing.

← Previous revision		Revision as of 15:42, 24 November 2023
Line 1:		Line 1:
	The '''Fast-Folding Algorithm''' (FFA) is a computational method primarily utilized in the domain of astronomy for detecting periodic signals.		The '''Fast-Folding Algorithm''' (FFA) is a computational method primarily utilized in the domain of astronomy for detecting periodic signals.
	<ref name=":0">{{Cite journal \|last=Parent \|first=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|url=http://dx.doi.org/10.3847/1538-4357/aac5f0 \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357}}</ref>		<ref name=":0">{{Cite journal \|last=Parent \|first=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|url=http://dx.doi.org/10.3847/1538-4357/aac5f0 \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357}}</ref>
	FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":0" />		FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":0" />
	A quintessential application of FFA is in the detection and analysis of [[Pulsar\|pulsars]]—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />		A quintessential application of FFA is in the detection and analysis of [[Pulsar\|pulsars]]—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />

	== History of the FFA[edit] ==		== History of the FFA[edit] ==

Phil074: Eliminated duplication in refs, added ref for Staelin (1969).

2023-11-24T15:36:16Z

Eliminated duplication in refs, added ref for Staelin (1969).

← Previous revision		Revision as of 15:36, 24 November 2023
Line 1:		Line 1:
			The '''Fast-Folding Algorithm''' (FFA) is a computational method primarily utilized in the domain of astronomy for detecting periodic signals.
	The '''Fast-Folding Algorithm''' (FFA) is a computational method primarily utilized in the domain of astronomy for detecting periodic signals.<ref name=":0">{{Cite journal \|last=Parent \|first=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|url=http://dx.doi.org/10.3847/1538-4357/aac5f0 \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357}}</ref> FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":1">{{Cite journal \|last=Parent \|first=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|url=https://iopscience.iop.org/article/10.3847/1538-4357/aac5f0 \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357}}</ref> A quintessential application of FFA is in the detection and analysis of [[Pulsar\|pulsars]]—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />
			<ref name=":0">{{Cite journal \|last=Parent \|first=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|url=http://dx.doi.org/10.3847/1538-4357/aac5f0 \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357}}</ref>
			FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":0" />
			A quintessential application of FFA is in the detection and analysis of [[Pulsar\|pulsars]]—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />

	== History of the FFA[edit] ==		== History of the FFA[edit] ==
	The Fast Folding Algorithm (FFA) has its roots dating back to 1969 when it was introduced by Professor David H. Staelin from the [[Massachusetts Institute of Technology\|Massachusetts Institute of Technology (MIT)]]. At the time, the scientific community was deeply involved in the study of pulsars, which are rapidly rotating [[Neutron star\|neutron stars]] emitting beams of electromagnetic radiation. Professor Staelin recognized the potential of the FFA as a powerful instrument for detecting periodic signals within these pulsar surveys. These surveys were not just about understanding pulsars but held a much broader significance. They played a pivotal role in testing and validating Einstein's [[General relativity\|theory of general relativity]], a cornerstone in the field of [[Astronomy]]. As the years progressed, the FFA saw various refinements, with researchers making tweaks and optimizations to enhance its efficiency and accuracy. Despite its potential, the FFA was mostly underutilized thanks to the dominance of [[Fast Fourier transform\|Fast Fourier Transform (FFT)]]-based techniques, which were the preferred choice for many in [[signal processing]] during that era. As a result, while the FFA showed promise, its applications in the broader scientific community remained underutilized for several decades.<ref name=":0~~" /><ref name=":1~~" />		The Fast Folding Algorithm (FFA) has its roots dating back to 1969 when it was introduced by Professor [[David H. Staelin]] from the [[Massachusetts Institute of Technology\|Massachusetts Institute of Technology (MIT)]].
			<ref name=":1">{{Citation \| last=Staelin \| first=David H. \| title=Fast Folding Algorithm for Detection of Periodic Pulse Trains \| journal=Proceedings of the IEEE \| volume=57 \| issue=4 \| pages=724–5 \| date=1969 \|doi=10.1109/PROC.1969.7051\| bibcode=1969IEEEP..57..724S }}</ref>
			At the time, the scientific community was deeply involved in the study of pulsars, which are rapidly rotating [[Neutron star\|neutron stars]] emitting beams of electromagnetic radiation. Professor Staelin recognized the potential of the FFA as a powerful instrument for detecting periodic signals within these pulsar surveys. These surveys were not just about understanding pulsars but held a much broader significance. They played a pivotal role in testing and validating Einstein's [[General relativity\|theory of general relativity]], a cornerstone in the field of [[Astronomy]]. As the years progressed, the FFA saw various refinements, with researchers making tweaks and optimizations to enhance its efficiency and accuracy. Despite its potential, the FFA was mostly underutilized thanks to the dominance of [[Fast Fourier transform\|Fast Fourier Transform (FFT)]]-based techniques, which were the preferred choice for many in [[signal processing]] during that era. As a result, while the FFA showed promise, its applications in the broader scientific community remained underutilized for several decades.<ref name=":0" />

	== Technical Foundations of the FFA[edit] ==		== Technical Foundations of the FFA[edit] ==
	The Fast Folding Algorithm (FFA) was initially developed as a method to search for periodic signals amidst noise in the [[time domain]], contrasting with the FFT search technique that operates in the [[frequency domain]]. The primary advantage of the FFA is its efficiency in avoiding redundant summations (unnecessary additional computations). Specifically, the FFA is much faster than standard folding at all possible trial periods, achieving this by performing summations through N×log2(N/p−1) steps rather than N×(N/p−1). This efficiency arises because the logarithmic term log2(N/p−1) grows much slower than the linear term (N/p−1), making the number of steps more manageable as N increases,N represents the number of samples in the [[time series]], and p is the trial folding period in units of samples. The FFA method involves folding each time series at multiple periods, performing partial summations in a series of log2(p) stages, and combining those sums to fold the data with a trial period between p and p+1. This approach retains all harmonic structures, making it especially effective for identifying narrow-pulsed signals in the long-period regime. One of the FFA's unique features is its hierarchical approach to folding, breaking the data down into smaller chunks, folding these chunks, and then combining them. This method, combined with its inherent tolerance to noise and adaptability for different types of data and hardware configurations, ensures the FFA remains a powerful tool for detecting periodic signals, especially in environments with significant noise or interference which makes it especially useful for Astronomical endavours.<ref name=":0~~" /><ref name=":1~~" />{{Short description\|Method for detecting periodic signals}}		The Fast Folding Algorithm (FFA) was initially developed as a method to search for periodic signals amidst noise in the [[time domain]], contrasting with the FFT search technique that operates in the [[frequency domain]]. The primary advantage of the FFA is its efficiency in avoiding redundant summations (unnecessary additional computations). Specifically, the FFA is much faster than standard folding at all possible trial periods, achieving this by performing summations through N×log2(N/p−1) steps rather than N×(N/p−1). This efficiency arises because the logarithmic term log2(N/p−1) grows much slower than the linear term (N/p−1), making the number of steps more manageable as N increases,N represents the number of samples in the [[time series]], and p is the trial folding period in units of samples. The FFA method involves folding each time series at multiple periods, performing partial summations in a series of log2(p) stages, and combining those sums to fold the data with a trial period between p and p+1. This approach retains all harmonic structures, making it especially effective for identifying narrow-pulsed signals in the long-period regime. One of the FFA's unique features is its hierarchical approach to folding, breaking the data down into smaller chunks, folding these chunks, and then combining them. This method, combined with its inherent tolerance to noise and adaptability for different types of data and hardware configurations, ensures the FFA remains a powerful tool for detecting periodic signals, especially in environments with significant noise or interference which makes it especially useful for Astronomical endavours.<ref name=":0" />{{Short description\|Method for detecting periodic signals}}
	In [[signal processing]], the '''fast folding algorithm''' ~~(Staelin,~~ ~~1969)~~ is an efficient [[algorithm]] for the detection of approximately-[[periodic function\|periodic]] events within [[time series]] data. It computes superpositions of the signal modulo various window sizes simultaneously.		In [[signal processing]], the '''fast folding algorithm'''<ref name=":1" /> is an efficient [[algorithm]] for the detection of approximately-[[periodic function\|periodic]] events within [[time series]] data. It computes superpositions of the signal modulo various window sizes simultaneously.

	The FFA is best known for its use in the detection of [[pulsar]]s, as popularised by [[SETI@home]] and [[Astropulse]].		The FFA is best known for its use in the detection of [[pulsar]]s, as popularised by [[SETI@home]] and [[Astropulse]].

WikiCleanerBot: v2.05b - Bot T5 CW#16 - Fix errors for CW project (Unicode control characters)

2023-11-19T01:37:04Z

v2.05b - Bot T5 CW#16 - Fix errors for CW project (Unicode control characters)

← Previous revision		Revision as of 01:37, 19 November 2023
Line 5:		Line 5:

	== Technical Foundations of the FFA[edit] ==		== Technical Foundations of the FFA[edit] ==
	The Fast Folding Algorithm (FFA) was initially developed as a method to search for periodic signals amidst noise in the [[time domain]], contrasting with the FFT search technique that operates in the [[frequency domain]]. The primary advantage of the FFA is its efficiency in avoiding redundant summations (unnecessary additional computations). Specifically, the FFA is much faster than standard folding at all possible trial periods, achieving this by performing summations through ~~N×log2~~(N/p−1) steps rather than N×(N/p−1). This efficiency arises because the logarithmic term ~~log2~~(N/p−1) grows much slower than the linear term (N/p−1), making the number of steps more manageable as N increases,N represents the number of samples in the [[time series]], and p is the trial folding period in units of samples. The FFA method involves folding each time series at multiple periods, performing partial summations in a series of ~~log2~~(p) stages, and combining those sums to fold the data with a trial period between p and p+1. This approach retains all harmonic structures, making it especially effective for identifying narrow-pulsed signals in the long-period regime. One of the FFA's unique features is its hierarchical approach to folding, breaking the data down into smaller chunks, folding these chunks, and then combining them. This method, combined with its inherent tolerance to noise and adaptability for different types of data and hardware configurations, ensures the FFA remains a powerful tool for detecting periodic signals, especially in environments with significant noise or interference which makes it especially useful for Astronomical endavours.<ref name=":0" /><ref name=":1" />{{Short description\|Method for detecting periodic signals}}		The Fast Folding Algorithm (FFA) was initially developed as a method to search for periodic signals amidst noise in the [[time domain]], contrasting with the FFT search technique that operates in the [[frequency domain]]. The primary advantage of the FFA is its efficiency in avoiding redundant summations (unnecessary additional computations). Specifically, the FFA is much faster than standard folding at all possible trial periods, achieving this by performing summations through N×log2(N/p−1) steps rather than N×(N/p−1). This efficiency arises because the logarithmic term log2(N/p−1) grows much slower than the linear term (N/p−1), making the number of steps more manageable as N increases,N represents the number of samples in the [[time series]], and p is the trial folding period in units of samples. The FFA method involves folding each time series at multiple periods, performing partial summations in a series of log2(p) stages, and combining those sums to fold the data with a trial period between p and p+1. This approach retains all harmonic structures, making it especially effective for identifying narrow-pulsed signals in the long-period regime. One of the FFA's unique features is its hierarchical approach to folding, breaking the data down into smaller chunks, folding these chunks, and then combining them. This method, combined with its inherent tolerance to noise and adaptability for different types of data and hardware configurations, ensures the FFA remains a powerful tool for detecting periodic signals, especially in environments with significant noise or interference which makes it especially useful for Astronomical endavours.<ref name=":0" /><ref name=":1" />{{Short description\|Method for detecting periodic signals}}
	In [[signal processing]], the '''fast folding algorithm''' (Staelin, 1969) is an efficient [[algorithm]] for the detection of approximately-[[periodic function\|periodic]] events within [[time series]] data. It computes superpositions of the signal modulo various window sizes simultaneously.		In [[signal processing]], the '''fast folding algorithm''' (Staelin, 1969) is an efficient [[algorithm]] for the detection of approximately-[[periodic function\|periodic]] events within [[time series]] data. It computes superpositions of the signal modulo various window sizes simultaneously.

← Previous revision		Revision as of 03:36, 24 December 2023
Line 2:		Line 2:
	<ref name=":0">{{Cite journal \|last=Parent \|first=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|url=http://dx.doi.org/10.3847/1538-4357/aac5f0 \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357\|doi-access=free }}</ref>		<ref name=":0">{{Cite journal \|last=Parent \|first=E. \|last2=Kaspi \|first2=V. M. \|last3=Ransom \|first3=S. M. \|last4=Krasteva \|first4=M. \|last5=Patel \|first5=C. \|last6=Scholz \|first6=P. \|last7=Brazier \|first7=A. \|last8=McLaughlin \|first8=M. A. \|last9=Boyce \|first9=M. \|last10=Zhu \|first10=W. W. \|last11=Pleunis \|first11=Z. \|last12=Allen \|first12=B. \|last13=Bogdanov \|first13=S. \|last14=Caballero \|first14=K. \|last15=Camilo \|first15=F. \|date=2018-06-29 \|title=The Implementation of a Fast-folding Pipeline for Long-period Pulsar Searching in the PALFA Survey \|url=http://dx.doi.org/10.3847/1538-4357/aac5f0 \|journal=The Astrophysical Journal \|volume=861 \|issue=1 \|pages=44 \|doi=10.3847/1538-4357/aac5f0 \|issn=1538-4357\|doi-access=free }}</ref>
	FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":0" />		FFA is designed to reveal repeating or cyclical patterns by "folding" data, which involves dividing the data set into numerous segments, aligning these segments to a common phase, and summing them together to enhance the signal of periodic events. This [[algorithm]] is particularly advantageous when dealing with non-uniformly sampled data or signals with a drifting period, which refer to signals that exhibit a frequency or period drifting over space and time, such cycles are not stable and consistent; rather, they are randomized.<ref name=":0" />
	A quintessential application of FFA is in the detection and analysis of [[~~Pulsar\|pulsars~~]]~~—highly~~ magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />		A quintessential application of FFA is in the detection and analysis of [[pulsar]]s—highly magnetized, rotating neutron stars that emit beams of [[electromagnetic radiation]]. By employing FFA, astronomers can effectively distinguish noisy data to identify the regular pulses of radiation emitted by these celestial bodies. Moreover, the Fast-Folding Algorithm is instrumental in detecting long-period signals, which is often a challenge for other algorithms like the [[Fast Fourier transform\|FFT]] (Fast-Fourier Transform) that operate under the assumption of a constant frequency. Through the process of folding and summing data segments, FFA provides a robust mechanism for unveiling periodicities despite noisy observational data, thereby playing a pivotal role in advancing our understanding of pulsar properties and behaviors.<ref name=":0" />

	== History of the FFA[edit] ==		== History of the FFA[edit] ==
	The Fast Folding Algorithm (FFA) has its roots dating back to 1969 when it was introduced by Professor [[David H. Staelin]] from the [[Massachusetts Institute of Technology\|Massachusetts Institute of Technology (MIT)]].		The Fast Folding Algorithm (FFA) has its roots dating back to 1969 when it was introduced by Professor [[David H. Staelin]] from the [[Massachusetts Institute of Technology\|Massachusetts Institute of Technology (MIT)]].
	<ref name=":1">{{Citation \| last=Staelin \| first=David H. \| title=Fast Folding Algorithm for Detection of Periodic Pulse Trains \| journal=Proceedings of the IEEE \| volume=57 \| issue=4 \| pages=724–5 \| date=1969 \|doi=10.1109/PROC.1969.7051\| bibcode=1969IEEEP..57..724S }}</ref>		<ref name=":1">{{Citation \| last=Staelin \| first=David H. \| title=Fast Folding Algorithm for Detection of Periodic Pulse Trains \| journal=Proceedings of the IEEE \| volume=57 \| issue=4 \| pages=724–5 \| date=1969 \|doi=10.1109/PROC.1969.7051\| bibcode=1969IEEEP..57..724S }}</ref>
	At the time, the scientific community was deeply involved in the study of pulsars, which are rapidly rotating [[~~Neutron~~ star~~\|neutron stars~~]] emitting beams of electromagnetic radiation. Professor Staelin recognized the potential of the FFA as a powerful instrument for detecting periodic signals within these pulsar surveys. These surveys were not just about understanding pulsars but held a much broader significance. They played a pivotal role in testing and validating Einstein's [[General relativity\|theory of general relativity]], a cornerstone in the field of [[Astronomy]]. As the years progressed, the FFA saw various refinements, with researchers making tweaks and optimizations to enhance its efficiency and accuracy. Despite its potential, the FFA was mostly underutilized thanks to the dominance of [[Fast Fourier transform\|Fast Fourier Transform (FFT)]]-based techniques, which were the preferred choice for many in [[signal processing]] during that era. As a result, while the FFA showed promise, its applications in the broader scientific community remained underutilized for several decades.<ref name=":0" />		At the time, the scientific community was deeply involved in the study of pulsars, which are rapidly rotating [[neutron star]]s emitting beams of electromagnetic radiation. Professor Staelin recognized the potential of the FFA as a powerful instrument for detecting periodic signals within these pulsar surveys. These surveys were not just about understanding pulsars but held a much broader significance. They played a pivotal role in testing and validating Einstein's [[General relativity\|theory of general relativity]], a cornerstone in the field of [[Astronomy]]. As the years progressed, the FFA saw various refinements, with researchers making tweaks and optimizations to enhance its efficiency and accuracy. Despite its potential, the FFA was mostly underutilized thanks to the dominance of [[Fast Fourier transform\|Fast Fourier Transform (FFT)]]-based techniques, which were the preferred choice for many in [[signal processing]] during that era. As a result, while the FFA showed promise, its applications in the broader scientific community remained underutilized for several decades.<ref name=":0" />

	== Technical Foundations of the FFA[edit] ==		== Technical Foundations of the FFA[edit] ==
	The Fast Folding Algorithm (FFA) was initially developed as a method to search for periodic signals amidst noise in the [[time domain]], contrasting with the FFT search technique that operates in the [[frequency domain]]. The primary advantage of the FFA is its efficiency in avoiding redundant summations (unnecessary additional computations). Specifically, the FFA is much faster than standard folding at all possible trial periods, achieving this by performing summations through N×log2(N/p−1) steps rather than N×(N/p−1). This efficiency arises because the logarithmic term log2(N/p−1) grows much slower than the linear term (N/p−1), making the number of steps more manageable as N increases,N represents the number of samples in the [[time series]], and p is the trial folding period in units of samples. The FFA method involves folding each time series at multiple periods, performing partial summations in a series of log2(p) stages, and combining those sums to fold the data with a trial period between p and p+1. This approach retains all harmonic structures, making it especially effective for identifying narrow-pulsed signals in the long-period regime. One of the FFA's unique features is its hierarchical approach to folding, breaking the data down into smaller chunks, folding these chunks, and then combining them. This method, combined with its inherent tolerance to noise and adaptability for different types of data and hardware configurations, ensures the FFA remains a powerful tool for detecting periodic signals, especially in environments with significant noise or interference which makes it especially useful for Astronomical endavours.<ref name=":0" />{{Short description\|Method for detecting periodic signals}}		The Fast Folding Algorithm (FFA) was initially developed as a method to search for periodic signals amidst noise in the [[time domain]], contrasting with the FFT search technique that operates in the [[frequency domain]]. The primary advantage of the FFA is its efficiency in avoiding redundant summations (unnecessary additional computations). Specifically, the FFA is much faster than standard folding at all possible trial periods, achieving this by performing summations through N×log2(N/p−1) steps rather than N×(N/p−1). This efficiency arises because the logarithmic term log2(N/p−1) grows much slower than the linear term (N/p−1), making the number of steps more manageable as N increases, N represents the number of samples in the [[time series]], and p is the trial folding period in units of samples. The FFA method involves folding each time series at multiple periods, performing partial summations in a series of log2(p) stages, and combining those sums to fold the data with a trial period between p and p+1. This approach retains all harmonic structures, making it especially effective for identifying narrow-pulsed signals in the long-period regime. One of the FFA's unique features is its hierarchical approach to folding, breaking the data down into smaller chunks, folding these chunks, and then combining them. This method, combined with its inherent tolerance to noise and adaptability for different types of data and hardware configurations, ensures the FFA remains a powerful tool for detecting periodic signals, especially in environments with significant noise or interference which makes it especially useful for Astronomical endavours.<ref name=":0" />{{Short description\|Method for detecting periodic signals}}
	In [[signal processing]], the '''fast folding algorithm'''<ref name=":1" /> is an efficient [[algorithm]] for the detection of approximately-[[periodic function\|periodic]] events within [[time series]] data. It computes superpositions of the signal modulo various window sizes simultaneously.		In [[signal processing]], the '''fast folding algorithm'''<ref name=":1" /> is an efficient [[algorithm]] for the detection of approximately-[[periodic function\|periodic]] events within [[time series]] data. It computes superpositions of the signal modulo various window sizes simultaneously.