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Quadratic time-frequency analysis methods produce spectrograms, which are 2D matrices. Interpreting 2D spectrograms quantitatively might not be straightforward. However, you can use the LabVIEW Time Frequency Analysis Tools to apply post-processing techniques to extract useful 1D information from spectrograms and compute the mean instantaneous frequency (MIF), the mean instantaneous bandwidth (MIB), the group delay, and the marginal integration from spectrograms. You can use these results to characterize spectrograms and to help with further feature extraction and pattern recognition in real-world applications. For example, you can use the MIF of ground echo signals to detect the liquefaction that might be associated with an earthquake, and you can use the MIF and MIB of Doppler ultrasound signals for noninvasive blood flow measurements.

The mean frequency of a signal describes the center of gravity of the power spectrum of the signal. The power spectrum of nonstationary signals is time dependent, and therefore the mean frequency of nonstationary signals is time dependent. The time-dependent mean frequency is called the mean instantaneous frequency. For nonstationary signals with a single frequency component or a single frequency band, the MIF describes the central frequency evolution over time.

Use the TFA Mean Instantaneous Frequency VI to compute the statistical first moment of the spectrogram along the frequency axis as an estimation of the MIF. The first moment of the Wigner-Ville Distribution (WVD) or the first moment of the Choi-Williams Distribution (CWD) is the MIF. The first moments of other quadratic time-frequency representations can provide only an approximation of the MIF.

The mean bandwidth of a signal describes the spread of the power spectrum of the signal around the mean frequency. The power spectrum of nonstationary signals is time dependent, and therefore the mean bandwidth of nonstationary signals is time dependent. The time-dependent mean bandwidth is called the mean instantaneous bandwidth.

Use the TFA Mean Instantaneous Bandwidth VI to compute the second moment of the spectrogram along the frequency axis as an estimation of the MIB.

The time delay of a single-tone signal describes the localization of the signal in the time domain. If signal A has a larger time delay than signal B, signal A follows signal B in the time domain. The group delay is the time delay of a nonstationary signal as a function of frequency. The group delay describes the time lags among different frequencies. You also can use the group delay to measure the propagation time through a system as a function of frequency.

Use the TFA Group Delay VI to compute the first moment of the spectrogram along the time axis as an estimation of the group delay.

The marginal integration is the integration of the spectrogram along the time axis or the frequency axis. If the integration along the time axis equals the power spectrum of the signal, the spectrogram satisfies the marginal frequency condition. If the integration along the frequency axis equals the instantaneous power of the signal, the spectrogram satisfies the marginal time condition. The WVD and the CWD satisfy both marginal conditions. For other quadratic time-frequency analysis methods, you can consider the marginal time integration as the mean instantaneous power and the marginal frequency integration as the mean power spectrum.

Use the TFA Marginal Integration VI to compute the marginal integration.

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