Time-frequency distributions that preserve energy variations

We present and illustrate the shortcomings of Cohen´s (1989) class of bilinear time-frequency distributions (BTFD) in preserving short-time energy variations of the individual frequency components of a multi-component signal. We then define a suitable energy variation property and derive a constraint on the BTFD kernel which is necessary and sufficient for this energy variation property. To satisfy the constraints exactly, the kernel must be signal dependent. We conclude that positive time-frequency distributions, which have signal-dependent kernels, may provide the best approach to the exact solution to this problem