Warped Wavelet Bases: Unitary Equivalence and Signal Processing
Baraniuk, Richard G.
Jones, Douglas L.
unitary operator theory; time frequency analysis
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.