An ultra-precise fast Fourier transform
The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating a computationally efficient estimate of the frequency content of a time series. Its limitations include: (1) information is only provided at discrete frequency steps, so further calculation, for example interp...
| Main Author: | |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2024
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| _version_ | 1811139384572903424 |
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| author | Henry, M |
| author_facet | Henry, M |
| author_sort | Henry, M |
| collection | OXFORD |
| description | The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating a computationally efficient estimate of the frequency content of a time series. Its limitations include: (1) information is only provided at discrete frequency steps, so further calculation, for example interpolation, may be required to obtain improved estimates of peak frequencies and amplitudes; (2) ‘energy’ from spectral peaks may ‘leak’ into adjacent frequencies, potentially causing lower amplitude peaks to be distorted or hidden; (3) the FFT is a discrete time approximation of continuous time mathematics. A new FFT calculation addresses each of these issues through the use of two windowing functions, derived from Prism Signal Processing. Separate FFT results are obtained by applying each windowing function to the data set. Calculations based on the two FFT results yields high precision estimates of spectral peak location (frequency) amplitude and phase while suppressing spectral leakage. |
| first_indexed | 2024-09-25T04:05:14Z |
| format | Journal article |
| id | oxford-uuid:7638c0e4-98b6-4bd7-87a4-b0b9662abda3 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:05:14Z |
| publishDate | 2024 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:7638c0e4-98b6-4bd7-87a4-b0b9662abda32024-05-20T07:13:22ZAn ultra-precise fast Fourier transformJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7638c0e4-98b6-4bd7-87a4-b0b9662abda3EnglishSymplectic ElementsElsevier2024Henry, MThe Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating a computationally efficient estimate of the frequency content of a time series. Its limitations include: (1) information is only provided at discrete frequency steps, so further calculation, for example interpolation, may be required to obtain improved estimates of peak frequencies and amplitudes; (2) ‘energy’ from spectral peaks may ‘leak’ into adjacent frequencies, potentially causing lower amplitude peaks to be distorted or hidden; (3) the FFT is a discrete time approximation of continuous time mathematics. A new FFT calculation addresses each of these issues through the use of two windowing functions, derived from Prism Signal Processing. Separate FFT results are obtained by applying each windowing function to the data set. Calculations based on the two FFT results yields high precision estimates of spectral peak location (frequency) amplitude and phase while suppressing spectral leakage. |
| spellingShingle | Henry, M An ultra-precise fast Fourier transform |
| title | An ultra-precise fast Fourier transform |
| title_full | An ultra-precise fast Fourier transform |
| title_fullStr | An ultra-precise fast Fourier transform |
| title_full_unstemmed | An ultra-precise fast Fourier transform |
| title_short | An ultra-precise fast Fourier transform |
| title_sort | ultra precise fast fourier transform |
| work_keys_str_mv | AT henrym anultraprecisefastfouriertransform AT henrym ultraprecisefastfouriertransform |