TFA Fast Gabor Spectrogram VI
- Updated2024-07-30
- 3 minute(s) read
Decomposes a signal as a linear combination of Gaussian Gabor elementary functions. After decomposing the signal, this VI adds the Wigner-Ville Distribution (WVD) and cross WVD of the elementary functions to compute the quadratic time-frequency representation of signal. Wire data to the signal input to determine the polymorphic instance to use or manually select the instance.
TFA Fast Gabor Spectrogram Details
The Gabor spectrogram has better time-frequency resolution than the STFT spectrogram method and less cross-term interference than the WVD method. The Gabor spectrogram also allows control of the tradeoff between the cross-term suppression and the joint time-frequency resolution.
The Gabor spectrogram also is called the Gabor expansion-based spectrogram. You can use the Gabor expansion to represent the signal as the linear combination of the time-frequency elementary functions, as shown in the following equation:
where hm,n(i) is the elementary function, and Cm,n is the Gabor coefficients.
After you represent the signal as the linear combination of the time-frequency elementary function, you can use the following equation to compute the WVD of the signal:
Thus, any two elementary functions generate the cross-term interferences. Instead of computing the WVD for any pair of elementary functions, you can select a subset for the computation based on the Manhattan distance 
between the pair of 
and 
. The resulting time-frequency distribution is the Gabor spectrogram, as defined in the following equation:
where D denotes the order. The joint time-frequency resolution and the cross-term interference of the Gabor spectrogram increases with order. When order is 0, the Gabor spectrogram is non-negative and is similar to the STFT spectrogram. As order approaches infinity, the Gabor spectrogram converges to the WVD.
Refer to the book Introduction to Time-Frequency and Wavelet Transforms for more information about the Gabor expansion and transform.
Examples
Refer to the Liquefaction Detection VI in the labview\examples\Time Frequency Analysis\TFAApplications directory for an example of using the TFA Fast Gabor Spectrogram VI.