TFA Wigner-Ville Distribution VI

TFA Wigner-Ville Distribution Details

The WVD is one of the quadratic time-frequency representation methods. The WVD has better joint time-frequency resolution than the short-time Fourier transform (STFT) spectrogram, whose resolution the window effect limits. You can compute the WVD by applying the fast Fourier transform (FFT) on the time-dependent autocorrelation as shown in the following equation:

where is the time-dependent autocorrelation of the signal s(t) defined by the following equation:

The WVD has the best joint time-frequency resolution among all known quadratic joint time-frequency analysis methods. It also preserves many useful properties, such as the time marginal condition as follows:

and the frequency marginal condition as follows:

However, signal components with a different central time or central frequency generate cross-term interference in the WVD. The cross-term interference reduces the readability of the time-frequency representation. Because real-valued signals have symmetric positive and negative frequency components, cross-term interference exists between the positive frequency components and the negative frequency components in the WVD of real-valued signals. If you convert real-valued signals into analytic signals, this VI suppresses the cross-term interference between the positive frequency components and the negative frequency components because analytic signals have only the positive frequency components of real-valued signals.

You can consider the Cohen's class distributions (the Choi-Williams Distribution and the Cone-Shaped Distribution) and the STFT spectrogram as the smoothed versions of the WVD. These time-frequency distributions suppress the cross-term interference, but they also lose some useful properties of the WVD and produce a degraded time-frequency resolution. Use the WVD if you need a high time-frequency resolution and the frequency components of the signal are relatively simple. If harmonics or other types of complicated frequency components exist in the signal, use the Cohen's class distributions or Gabor spectrogram to suppress the cross-term interference.

Examples

Refer to the following VIs for examples of using the TFA Wigner-Ville Distribution VI:

• Marginal Condition VI: labview\examples\Time Frequency Analysis\TFAFunctions
• Pseudo Wigner-Ville Distribution VI: labview\examples\Time Frequency Analysis\TFAFunctions