Title :
On joint distributions for arbitrary variables
Author :
Baraniuk, Richard G. ; Cohen, Leon
Author_Institution :
Dept. of Electr. & Comput. Eng., Rice Univ., Houston, TX, USA
Abstract :
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.<>
Keywords :
mathematical operators; signal processing; statistical analysis; arbitrary variables; commutator; frequency; joint distributions; signal analysis; signal processing; time; unitary characteristic function operator; unitary transformation; Eigenvalues and eigenfunctions; Integral equations; Quantum mechanics; Time frequency analysis;
Journal_Title :
Signal Processing Letters, IEEE
