Adaptive time-frequency transform

  • Authors:

  • Stephane Mallat;Zhifeng Zhang

  • Affiliations:

  • Courant Institute, New York University, New York, NY;Courant Institute, New York University, New York, NY

  • Venue:
  • ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: digital speech processing - Volume III
  • Year:
  • 1993

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Abstract

A matching pursuit decomposes any signal into a linear expansion of waveforms that belong to a dictionary of functions. These waveforms are selected in order to best match the signal structures. For dictionaries of functions that have a wide range of different time-frequency localization, a matching pursuit yields an adaptive timefrequency transform. We derive a signal energy distribution in the time-frequency plane, which does not include interference terms, unlike Wigner and Cohen class distributions. Signal components that are coherent with respect to the dictionary can be extracted. An application to noise removal is described.