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Reduced Interference Time-Frequency Distributions: Scaled Decompositions and Interpretations

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Book cover Wavelet Transforms and Time-Frequency Signal Analysis

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

Many time-frequency representations fail to capture the full local and global character of signals. Examples of deficiencies are presented, and possible solutions that utilize special sets of orthonormally related windows to realize Cohen’s class of time-frequency distributions (TFDs) are proposed. 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) distinct windows for an overall analysis of N + 1 points, where N = 2n, and n is a positive integer. Application of this theory offers very fast computation of TFDs since very few analysis windows are needed, and fast, recursive, STFT algorithms can be used.

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Authors
  1. William J. Williams
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, Fl, 32816, USA

    Lokenath Debnath

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© 2001 Springer Science+Business Media New York

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Williams, W.J. (2001). Reduced Interference Time-Frequency Distributions: Scaled Decompositions and Interpretations. In: Debnath, L. (eds) Wavelet Transforms and Time-Frequency Signal Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0137-3_12

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  • DOI: https://doi.org/10.1007/978-1-4612-0137-3_12

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6629-7

  • Online ISBN: 978-1-4612-0137-3

  • eBook Packages: Springer Book Archive

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