Fractional-Fourier-domain weighted Wigner distribution
Abstract
A fractional-Fourier-domain realization of the weighted Wigner distribution (or S-method), producing auto-terms close to the ones in the Wigner distribution itself, but with reduced cross-terms, is presented. The computational cost of this fractional-domain realization is the same as the computational cost of the realizations in the time or the frequency domain, since the short-time Fourier transform of the fractional Fourier transform of a signal corresponds to the short-time Fourier transform of the signal itself, with the window being the fractional Fourier transform of the initial one. The appropriate fractional domain is found from the analysis of the second-order fractional Fourier transform moments. Numerical simulations show a qualitative advantage in the time-frequency representation, when the calculation is done in the optimal fractional domain.
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For mono-component signals, the required fractional Fourier transformation order can be found based on the fractional moments of the signal.
“Alternatively, for mono-component signals, the required fractional Fourier transformation order can also be found based on the fractional moments of the signal.”
From Short-time fourier transform: two fundamental properties and an optimal implementation (2003) · cites this paper as [35]
Cites
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
A method for time-frequency analysis
Stanković, L. (1994) · IEEE Transactions on Signal Processing · doi:10.1109/78.258146 · Cited by 403 · see citing works
An adaptive optimal-kernel time-frequency representation
Jones, D. L., & Baraniuk, R. G. (1995) · IEEE Transactions on Signal Processing · doi:10.1109/78.469854 · Cited by 389 · 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
Kernel design for time-frequency signal analysis using the Radon transform
Ristić, B., & Boashash, B. (1993) · IEEE Transactions on Signal Processing · doi:10.1109/78.215325 · Cited by 97 · see citing works
Boashash, B., & Ristić, B. (1998) · Signal Processing · doi:10.1016/s0165-1684(98)00018-8 · Cited by 83 · see citing works
Pseudo affine Wigner distributions: definition and kernel formulation
Gonçalvès, P., & Baraniuk, R. G. (1998) · IEEE Transactions on Signal Processing · doi:10.1109/78.678464 · Cited by 74 · see citing works
An analysis of some time-frequency and time-scale distributions
Stanković, L. (1994) · Annals of Telecommunications · doi:10.1007/bf02999442 · Cited by 70 · see citing works
On fractional Fourier transform moments
Alieva, T., & Bastiaans, M. J. (2000) · IEEE Signal Processing Letters · doi:10.1109/97.873570 · Cited by 69 · see citing works
Self-citationToeplitz and Hankel kernels for estimating time-varying spectra of discrete-time random processes
Scharf, L. L., & Friedlander, B. (2001) · IEEE Transactions on Signal Processing · doi:10.1109/78.890359 · Cited by 61 · see citing works
On generalized-marginal time-frequency distributions
Xia, X., Owechko, Y., Soffer, B. H., & Matic, R. M. (1996) · IEEE Transactions on Signal Processing · doi:10.1109/78.542448 · Cited by 39 · see citing works
A high resolution time frequency representation with significantly reduced cross-terms
Özdemir, A. K., & Arıkan, O. (2002) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp.2000.859054 · Cited by 16 · see citing works
Generalized-marginal time-frequency distributions
Xia, X., Owechko, Y., Soffer, B. H., & Matic, R. M. (1996) · IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis · doi:10.1109/tfsa.1996.550104 · Cited by 11 · see citing works
A new kind of windowed fractional transforms
Zhang, Y., Gu, B., Dong, B., & Yang, G. (1998) · Optics Communications · doi:10.1016/s0030-4018(98)00158-8 · Cited by 8 · see citing works
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Time–frequency feature representation using energy concentration: An overview of recent advances
Sejdić, E., Djurović, I., & Jiang, J. (2008) · Digital Signal Processing · doi:10.1016/j.dsp.2007.12.004 · Cited by 756 · see citing works
Fractional Fourier transform as a signal processing tool: An overview of recent developments
Sejdić, E., Djurović, I., & Stanković, L. (2010) · Signal Processing · doi:10.1016/j.sigpro.2010.10.008 · Cited by 425 · see citing works
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
Time–frequency signal analysis based on the windowed fractional Fourier transform
Stanković, L., Alieva, T., & Bastiaans, M. J. (2003) · Signal Processing · doi:10.1016/s0165-1684(03)00197-x · Cited by 110 · see citing works
Self-citationOn rotated time-frequency kernels
Bastiaans, M. J., Alieva, T., & Stanković, L. (2002) · IEEE Signal Processing Letters · doi:10.1109/lsp.2002.805118 · Cited by 53 · see citing works
Self-citationImplementation of Different Non-recursive FIR Band-Pass Filters Using Fractional Fourier Transform
Chaturvedi, S., Kumar, M., Parmar, G., & Shukla, P. (2012) · International Conference on Computational Intelligence and Communication Networks (CICN) · doi:10.1109/cicn.2012.131 · Cited by 5 · see citing works
Implementation and Realization of TFDs
(2003) · Elsevier eBooks · doi:10.1016/b978-008044335-5/50027-9 · Cited by 3 · see citing works
Advanced Implementation and Realization of TFDs
Boashash, B., Putland, G. R., Stanković, L., Bastiaans, M. J., Van Leest, A. J., Williams, W. J., Aviyente, S., Putland, G. R., & O’Toole, J. M. (2016) · Elsevier eBooks · doi:10.1016/b978-0-12-398499-9.00006-6 · Cited by 1 · see citing works
Self-citationTime-frequency analysis of frequency-coded signals
Rogozovskyi, O. A., Stankoviae, L., & Djuroviae, I. (2001) · MTS/IEEE OCEANS Conference (OCEANS) · doi:10.1109/oceans.2001.968215 · Cited by 1 · see citing works
(2003) · Elsevier eBooks · doi:10.1016/b978-008044335-5/50038-3
- Authors
- Stankovic, L., Alieva, T., & Bastiaans, M. J.
- Affiliations
- Eindhoven University of Technology (NL)
- ORCID
- Alieva, T.
- Venue
- Proceedings of the 11th IEEE Signal Processing Workshop on Statistical Signal Processing (Cat. No.01TH8563)
- Publisher
- IEEE
- Published
- 2002-11-13
- Pages
- 321-324
- ISSN
- 2373-0803 (ISSN-L)
- OpenAlex
- W2155487956
- Cited by
- 10
- References
- 14
- Citations by year
- 2016: 1 · 2012: 1
- FWCI
- 3.15
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- IEEE Statistical Signal Processing Workshop (SSP) (publishedVersion)
- TU/e Research Portal (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Computer Science › Signal Processing › Digital Filter Design and Implementation
- Physical Sciences › Engineering › Computational Mechanics › Sparse and Compressive Sensing Techniques
- Keywords
- S-method, fractional Fourier transform, time-frequency representation, short-time Fourier transform, second moment, computational cost
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