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.


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Inputs/Outputs

  • cnclst.png zoom settings —

    zoom settings specifies the frequency zoom factor and the zoom range.

  • ci32.png zoom factor —

    zoom factor specifies how much to zoom the spectrogram. zoom factor must be an integer greater than or equal to 1. The default is 1.

  • cdbl.png f0 —

    f0 specifies the lowest frequency in the resulting spectrogram in hertz. The default is NaN, which indicates that the lowest frequency equals 0 for real-valued input signals and that the lowest frequency equals -fs/2 for complex-valued input signals, where fs is the sampling rate of the signal.

  • ci32.png number of bins —

    number of bins specifies the total number of frequency bins in the resulting spectrogram. As the value of number of bins increases, the frequency range of spectrogram increases. The default value is -1, which specifies that the frequency range of spectrogram is from f0 to fs/2, where fs is the sampling rate of the signal. number of bins must not be greater than half of zoom factorxfrequency bins for real-valued input signals and must not be greater than zoom factorxfrequency bins for complex-valued input signals.

  • ci32.png order —

    order specifies how this VI balances the time-frequency resolution and the cross-term interference of the Gabor spectrogram. order must be greater than or equal to 0, or this VI sets order to 0 automatically.

  • 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.

  • ci32.png Gaussian window length —

    Gaussian window length specifies the length of the Gaussian window, in samples, of the Gabor elementary functions and controls the relationship between the time resolution and the frequency resolution of the spectrogram. Gaussian window length must be a power of 2 and greater than or equal to 8. As the value of Gaussian window length increases, the frequency resolution increases, but the time resolution decreases.

  • 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 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.