We discuss some issues relevant to time-frequency analysis. Among them are, time-frequency spatial/spatial-frequency representations, generalized marginals and generalized characteristic functions. We derive representations that jointly involve the four variables, time, frequency, space, and spatial frequency. We apply these representations to wave packet motion. For the study on generalized marginals we show that there is an inherent difference between the standard methods of transforming variables and in time- frequency analysis. We use the method of generalized characteristic function operator method to generalize Taylor's theorem.
Leon Cohen, Leon Cohen,
"Topics in time-frequency representations", Proc. SPIE 2846, Advanced Signal Processing Algorithms, Architectures, and Implementations VI, (22 October 1996); doi: 10.1117/12.255436; https://doi.org/10.1117/12.255436