Linear and quadratic time-frequency signal representations
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A tutorial review of both linear and quadratic representations is given. The linear representations discussed are the short-time Fourier transform and the wavelet transform. The discussion of quadratic representations concentrates on the Wigner distribution, the ambiguity function, smoothed versions of the Wigner distribution, and various classes of quadratic time-frequency representations. Examples of the application of these representations to typical problems encountered in time-varying signal processing are provided.>
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The discrete STFT can be efficiently implemented by using FFT techniques.
“where and are integers, and and are the sampling intervals of time and frequency, and it can be efficiently implemented by using FFT techniques.”
From Short-time fourier transform: two fundamental properties and an optimal implementation (2003) · cites this paper as [1]
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Flandrin, P. (2005) · ICASSP '84. IEEE International Conference on Acoustics, Speech, and Signal Processing · doi:10.1109/icassp.1984.1172741 · Cited by 239 · see citing works
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The fractional Fourier transform and time-frequency representations
Almeida, L. B. (1994) · IEEE Transactions on Signal Processing · doi:10.1109/78.330368 · Cited by 1,924 · see citing works
Digital computation of the fractional Fourier transform
Ozaktas, H. M., Arikan, O., Kutay, M. A., & Bozdagt, G. (1996) · IEEE Transactions on Signal Processing · doi:10.1109/78.536672 · Cited by 1,187 · see citing works
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Short-time fourier transform: two fundamental properties and an optimal implementation
Durak, L., & Arikan, O. (2003) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2003.810293 · Cited by 345 · see citing works
Discrete fractional Fourier-transform based on orthogonal projections
Pei, S.-C., Yeh, M.-H., & Tseng, C.-C. (1999) · IEEE Transactions on Signal Processing · doi:10.1109/78.757221 · Cited by 297 · see citing works
introduction to the fractional fourier transform and its applications
Ozaktas, H. M., Kutay, M. A., & Mendlovic, D. (1999) · Advances in Imaging and Electron Physics · doi:10.1016/s1076-5670(08)70272-6 · Cited by 164 · see citing works
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Machinery Diagnosis Based on Wavelet Packets
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- Authors
- Hlawatsch, F., & Boudreaux-Bartels, G. F.
- Affiliations
- University of Rhode Island (US)
- ORCID
- Hlawatsch, F.
- Venue
- IEEE Signal Processing Magazine
- Published
- 1992-04
- Volume
- 9
- Issue
- 2
- Pages
- 21-67
- ISSN
- 1053-5888 (ISSN-L)
- OpenAlex
- W2048508162
- Cited by
- 1,632
- References
- 1
- Citations by year
- 2026: 18 · 2025: 23 · 2024: 35 · 2023: 32 · 2022: 40 · 2021: 35 · 2020: 36 · 2019: 38 · 2018: 51 · 2017: 53 · 2016: 54 · 2015: 36 · 2014: 46 · 2013: 50 · 2012: 42
- FWCI
- 66.40
- Type
- journal article
- Language
- en
- Open access
- Locations
- IEEE Signal Processing Magazine (publishedVersion)
- Journal of Media Literacy Education (submittedVersion, cc-by)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Engineering › Computational Mechanics › Sparse and Compressive Sensing Techniques
- Physical Sciences › Computer Science › Signal Processing › Music and Audio Processing
- Keywords
- time-frequency representation, short-time Fourier transform, wavelet transform, Wigner function, ambiguity function
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