WARPED WAVELET BASES:  UNITARY EQUIVALENCE AND SIGNAL PROCESSING


Richard G. Baraniuk and Douglas L. Jones

Laboratoire de Physique (URA 1325 CNRS)
Ecole Normale Superieure de Lyon
46 allee d'Italie, 69364 Lyon Cedex 07, 
France 

Coordinated Science Laboratory
University of Illinois, Urbana, IL 61801, USA


The notions of time, frequency, and scale are generalized using
concepts from unitary operator theory and applied to time-frequency 
analysis, in particular the wavelet and short-time Fourier transform 
orthonormal bases and Cohen's class of bilinear time-frequency 
distributions.  The result is an infinite number of new signal 
analysis and processing tools that are implemented simply by 
prewarping the signal by a unitary transformation, performing 
standard processing techniques on the warped signal, and then (in 
some cases) unwarping the resulting output.  These unitarily 
equivalent, warped signal representations are useful for representing 
signals that are well modeled by neither the constant-bandwidth
analysis of time-frequency techniques nor the proportional-bandwidth 
analysis of time-scale techniques.

Presented at ICASSP 1993 in Minneapolis, MN, March 1993