Warped perspectives in time-frequency analysis

Unitary similarity transformations furnish a simple yet powerful vehicle for generating new classes of joint distributions based on concepts different from time, frequency, and scale. These new signal representations focus on the critical characteristics of large classes of signals and, hence, prove useful for representing and processing signals that are not well matched by current techniques. In particular, we construct distributions to match almost any one-to-one group delay or instantaneous frequency characteristic. Amazingly, all distributions that have been used to illustrate more complicated generalized distribution design techniques can be generated using the unitary transformation method.