Optimal filtering in fractional Fourier domains

Date
1995
Advisor
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Source Title
International Conference on Acoustics, Speech and Signal Processing
Print ISSN
Electronic ISSN
Publisher
IEEE
Volume
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Pages
937 - 940
Language
English
Type
Conference Paper
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Abstract

The ordinary Fourier transform is suited best for analysis and processing of time-invariant signals and systems. When we are dealing with time-varying signals and systems, filtering in fractional Fourier domains might allow us to estimate signals with smaller minimum-mean-square error (MSE). We derive the optimal fractional Fourier domain filter that minimizes the MSE for given non-stationary signal and noise statistics, and time-varying distortion kernel. We present an example for which the MSE is reduced by a factor of 50 as a result of filtering in the fractional Fourier domain, as compared to filtering in the conventional Fourier or time domains. We also discuss how the fractional Fourier transformation can be computed in O(N log N) time, so that the improvement in performance is achieved with little or no increase in computational complexity.

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Keywords
Fractional Fourier domains, Minimum mean square error, Optimal filtering, Time varying signals, Wigner distribution, Algorithms, Computational complexity, Digital signal processing, Estimation, Fourier transforms, Frequency domain analysis, Mathematical models, Signal distortion, Spurious signal noise, Statistics, Time domain analysis, Time varying systems, Computer simulation, Errors, Parameter estimation, Signal interference, Signal theory, Signal filtering and prediction, Fractional Fourier domains, Minimum mean square error, Noise statistics, Optimal filtering, Time invariant signals and systems, Time varying distortion Kernel
Citation
Published Version (Please cite this version)