Gabor–Wigner transform

Since the Gabor transform does not have high clarity, and the Wigner distribution function has a "cross term problem" (i.e. is non-linear), a 2007 study by S. C. Pei and J. J. Ding proposed a new combination of the two transforms that has high clarity and no cross term problem.

[1] Since the cross term does not appear in the Gabor transform, the time frequency distribution of the Gabor transform can be used as a filter to filter out the cross term in the output of the Wigner distribution function.

The goal of filter design is to remove unwanted portions of the signal while preserving the necessary parts.

The purpose of modulation is to place a signal within a specific time or frequency range.

Using the Gabor–Wigner transform, we can simultaneously consider how to introduce more or more suitable signal patterns in both the time and frequency domains.