TSA Bispectrum VI
- Updated2024-07-30
- 3 minute(s) read
Computes the single-sided bispectrum of a univariate time series using the fast Fourier transform (FFT) or the autoregressive (AR) model based method. The bispectrum is a type of third-order spectrum, which is related to the third moment (skewness) of a time series. The resulting bispectrum can detect the asymmetric nonlinearities in the input time series. Wire data to the Xt input to determine the polymorphic instance to use or manually select the instance.
TSA Bispectrum Details
This VI computes the single-sided bispectrum of a univariate time series using the FFT based method according to the following equation:
S(f1, f2) = A[X(f1)X(f2)X*(f1+f2)]
A[X] denotes the averaging value of X. X(f) is the Fourier transform of the time series Xt according to the following equation.
where N is the number of frequency bins and fs is the sampling rate. Before computing the bispectrum, this VI adjusts the value of the window length, length, and the value of frequency bins according to the following table.
| signal block size | length | adjusted length | frequency bins | adjusted frequency bins |
|---|---|---|---|---|
| <=1024 | -1 | signal block size | -1 | signal block size |
| >1024 | -1 | 1024 | -1 | 1024 |
| arbitrary | arbitrary | no change | -1 | length |
| arbitrary | -1 | signal block size | <signal block size | signal block size |
| arbitrary | -1 | signal block size | >=signal block size | no change |
| arbitrary | arbitrary | no change | >=length | no change |
| arbitrary | arbitrary | no change | <length | length |
This VI computes the bispectrum of a univariate time series using the AR model based method according to the following equation:
S(f1, f2) = bA[X(f1)X(f2)X*(f1+f2)]
b is the third moment of estimated noise series of AR model.
s² is the noise variance of the estimated AR model of the time series and a is an array that contains the coefficients of the AR model. a=[1, a1, a2,… ,an], where n is AR order. Before computing the bispectrum, this VI wraps a to an N-point series a'.
Examples
Refer to the following VIs for examples of using the TSA Bispectrum VI:
- Bispectrum Analysis VI: labview\examples\Time Series Analysis\TSAGettingStarted
- Beam Crack Detection VI: labview\examples\Time Series Analysis\TSAApplications