Gabor-Wigner transform

The Gabor transform and the Wigner distribution function 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[2], 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[2]. 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

• Gabor transform

• Wigner distribution function

• Gabor-Wigner transform

There are many different combinations to define the Gabor-Wigner transform. Here four different definitions are given.

Performance of Gabor-Wigner transform

Here some examples are given to show the performance of four Gabor-Wigner transform comparing to Gabor transform and Wigner distribution function.

The above examples illustrate that the Gabor-Wigner transform has less cross term and higher clarity than Gabor transform.

See also

• Time-frequency representation
• Short-time Fourier transform
• Gabor transform
• Wigner distribution function

References

• Jian-Jiun Ding, Time frequency analysis and wavelet transform class note, the Department of Electrical Engineering, National Taiwan University (NTU), Taipei, Taiwan, 2007.
• S. C. Pei and J. J. Ding, “Relations between Gabor transforms and fractional Fourier transforms and their applications for signal processing,” IEEE Trans. Signal Processing, vol. 55, no. 10, pp. 4839-4850, Oct. 2007.