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Proceedings Paper

Minimal-window time-frequency distributions
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Paper Abstract

This paper outlines means of using special sets of orthonormally related windows to realize Cohen's class of time-frequency distributions (TFDs). This is accomplished by decomposing the kernel of the distribution in terms of the set of analysis windows to obtain short time Fourier transforms (STFTs). The STFTs obtained using these analysis windows are used to form spectrograms which are then linearly combined with proper weights to form the desired TFD. A set of orthogonal analysis windows which also have the scaling property proves to be very effective, requiring only 1 + log2(N - 1) distinct windows for an overall analysis of N + 1 points, where N equals 2n, with n a positive integer. Application of this theory offers very fast computation of TFDs, since very few analysis windows needed and fast, recursive STFT algorithms can be used. Additionally, it is shown that a minimal set of specially derived orthonormal windows can represent most TFDs, including Reduced Interference Distributions (RIDs) with only three distinct windows plus an impulse window. Finally, the Minimal Window RID (MW-RID) which achieves RID properties with only one distinct window and an impulse window is presented.

Paper Details

Date Published: 2 November 1999
PDF: 12 pages
Proc. SPIE 3807, Advanced Signal Processing Algorithms, Architectures, and Implementations IX, (2 November 1999); doi: 10.1117/12.367661
Show Author Affiliations
William J. Williams, Univ. of Michigan (United States)
Selin Aviyente, Univ. of Michigan (United States)


Published in SPIE Proceedings Vol. 3807:
Advanced Signal Processing Algorithms, Architectures, and Implementations IX
Franklin T. Luk, Editor(s)

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