14 November 1989 Novel Approach To Cross-Terms Elimination In Wigner Distribution Using Adaptive Filtering In Frequency Domain
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Abstract
The proposed adaptive filter approach for cross-terms elimination relies on the fact that the Wigner distribution (WD), when windowed in time, due to computations and availability problems, does not change its spectral characteristics at the signal frequencies. The only time-varying components, as the window slides on stationary data, are those corresponding to the signal cross-terms, where they exhibit a phase change. The constant and the time-varying behavior in Pseudo Wigner Distribution (PWD) can be distinguished by adaptive filtering. In this paper, frequency-domain least mean squares (LMS) algorithm is used to both track and suppress the cross-terms, and therefore, allows a much better reading of the time-varying distribution of power over frequency. In the adaptive filtering approach, the desired input (primary) takes the PWD's for different data blocks, while the filter input (reference) is assigned unit values. Due to the nature of the primary and reference data, the frequency domain filter adapts to the constant sinusoidal peak values. However, because of the uncorrelatedness, it fails to track the time-varying components in the desired signal, leaving out the cross-terms to propagate to the output filter error. The cross-correlation between the constant values in the reference and the time-varying components in the desired signal can be controlled by the mechanism by which the PWD's are generated. Random sliding over the data may show improved performance compared to regular sliding with disjoint or overlapping blocks.
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Moeness G. Amin, Moeness G. Amin, Fred Allen, Fred Allen, } "Novel Approach To Cross-Terms Elimination In Wigner Distribution Using Adaptive Filtering In Frequency Domain", Proc. SPIE 1152, Advanced Algorithms and Architectures for Signal Processing IV, (14 November 1989); doi: 10.1117/12.962302; https://doi.org/10.1117/12.962302
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