Optimal filtering in fractional Fourier domains

For time-invariant degradation models and stationary signals and noise, the classical Fourier domain Wiener filter, which can be implemented in O(N log N) time, gives the minimum mean-square-error estimate of the original undistorted signal. For time-varying degradations and nonstationary processes,...

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Bibliographic Details
Published in:IEEE transactions on signal processing 1997-05, Vol.45 (5), p.1129-1143
Main Authors: Kutay, A., Ozaktas, H.M., Ankan, O., Onural, L.
Format: Article
Language:English
Subjects:
1f noise
Applied sciences
Chirp
Convolution
Degradation
Detection, estimation, filtering, equalization, prediction
Digital filters
Exact sciences and technology
Filtering
Fourier transforms
Information, signal and communications theory
Optical filters
Optical noise
Signal and communications theory
Signal, noise
Telecommunications and information theory
Wiener filter
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Summary:For time-invariant degradation models and stationary signals and noise, the classical Fourier domain Wiener filter, which can be implemented in O(N log N) time, gives the minimum mean-square-error estimate of the original undistorted signal. For time-varying degradations and nonstationary processes, however, the optimal linear estimate requires O(N/sup 2/) time for implementation. We consider filtering in fractional Fourier domains, which enables significant reduction of the error compared with ordinary Fourier domain filtering for certain types of degradation and noise (especially of chirped nature), while requiring only O(N log N) implementation time. Thus, improved performance is achieved at no additional cost. Expressions for the optimal filter functions in fractional domains are derived, and several illustrative examples are given in which significant reduction of the error (by a factor of 50) is obtained.
ISSN:1053-587X
1941-0476
DOI:10.1109/78.575688