The Gabor transform, named after Dennis Gabor, and the Wigner distribution function, named after Eugene Wigner, are both tools for time-frequency analysis. 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. 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.

Mathematical definition

Character

Application

The Gabor–Wigner transform performs well in image processing, filter design, signal sampling, modulation, demodulation, speech processing, and biomedical engineering.

Filter Design

The goal of filter design is to remove unwanted portions of the signal while preserving the necessary parts. By using the Gabor–Wigner transform, we can simultaneously consider filters in both the time domain and frequency domain, representing a form of time-frequency analysis. The main concept is illustrated as follows.

Signal Modulation

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. Due to the absence of cross-term issues, it performs better than the Wigner transform. From the figure (WDF) above, it can also be observed that when using the Wigner transform (WDF), the generated cross-terms have a severe impact on modulation.

Technique for fast implementation of the Gabor-Wigner Transform

Comparison