Joint Distributions of Arbitrary Variables Made Easy

We propose a simple framework for studying certain 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, the method can generate many distributions previously attainable only by the general construction of Cohen, including distributions of time versus inverse frequency, time versus Mellin transform (scale), and time versus chirp. In addition to providing insight into these new signal analysis tools, warp-based distributions have efficient implementations for potential use in applications.