On joint distributions for arbitrary variables

There has been considerable interest in the problem of joint representations for variables other than time and frequency. We compare the methods of Cohen (1991) and of Baraniuk and Jones (see Proc. IEEE Int. Conf. Acoust., Speech Signal Processing, ICASSP '93, p.320-323, vol.III) and show their equivalence for variables that have the same commutator as time and frequency. In addition, we report the following very general result. All pairs of variables connected by a unitary transformation have joint distributions that are functionally equivalent.<
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