Unitary Equivalence and Signal Processing
Baraniuk, Richard G.
Jones, Douglas L.
The notions of time, frequency, and scale are generalized using concepts from unitary operator theory and eigenanalysis. 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 and processing signals that are not well matched by current techniques.