Minimal-window time-frequency distributions

William J. Williams; Selin Aviyente

doi:10.1117/12.367661

2 November 1999 Minimal-window time-frequency distributions

William J. Williams, Selin Aviyente

Proceedings Volume 3807, Advanced Signal Processing Algorithms, Architectures, and Implementations IX; (1999) https://doi.org/10.1117/12.367661
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

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.

Citation Download Citation

William J. Williams and Selin Aviyente "Minimal-window time-frequency distributions", Proc. SPIE 3807, Advanced Signal Processing Algorithms, Architectures, and Implementations IX, (2 November 1999); https://doi.org/10.1117/12.367661

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