Joint distributions of arbitrary variables made easy

The successful application of joint time-frequency distributions to problems in time-varying spectral analysis has stimulated considerable interest in distributions of other variables for use when a strict time-frequency analysis is not appropriate. Joint distributions generalise single variable distributions that measure the energy content of some physical quantity in a signal. We propose a new framework for studying joint distributions of variables beyond time-frequency and time-scale. When applicable, our results turn the theory of joint distributions of arbitrary variables into an easy exercise of coordinate transformation. While straightforward, our method can generate many distributions previously attainable only by the general method of Cohen (see Time-Frequency Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1995)