Computes the discrete Wigner-Ville Distribution (WVD) of signal. Wire data to the signal input to determine the polymorphic instance to use or manually select the instance.


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Inputs/Outputs

  • c1dcdb.png signal —

    signal specifies the input signal.

  • cnclst.png time-frequency sampling info —

    time-frequency sampling info specifies the density to use to sample the signal in the joint time-frequency domain and defines the size of the resulting 2D time-frequency array.

  • ci32.png time steps —

    time steps specifies the sampling period, in samples, along the time axis in the joint time-frequency domain. The default is -1, which specifies that this VI adjusts time steps automatically so that no more than 512 rows exist in spectrogram.

  • ci32.png frequency bins —

    frequency bins specifies the number of bins along the frequency axis to sample the signal in the joint time-frequency domain. frequency bins must be a power of 2 and greater than 0. The scale info output contains the actual sampling period in hertz along the frequency axis.

  • cerrcodeclst.png error in (no error) —

    error in describes error conditions that occur before this node runs. This input provides standard error in functionality.

  • cdbl.png sampling rate —

    sampling rate specifies the sampling rate of signal in hertz. sampling rate must be greater than 0, or this VI sets sampling rate to 1 automatically. The default is 1.

  • i2ddbl.png spectrogram —

    spectrogram returns the quadratic time-frequency representation of the signal. Each row corresponds to the instantaneous power spectrum at a certain time.

  • ifxdt.png scale info —

    scale info returns the time scale and the frequency scale information of the time-frequency representation, including the time offset, the time interval between every two contiguous rows, the frequency offset, and the frequency interval between every two contiguous columns of spectrogram. Use the TFA Get Time and Freq Scale Info VI to return detailed information about the time scale and the frequency scale.

  • ierrcodeclst.png error out —

    error out contains error information. This output provides standard error out functionality.

    • 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