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Owning Palette: Correlation and Spectral Analysis VIs

Installed With: Advanced Signal Processing Toolkit

Computes the single-sided bispectrum of an input 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.

Details  Examples

Use the pull-down menu to select an instance of this VI.

Select an instance TSA Bispectrum (waveform)TSA Bispectrum (array)

TSA Bispectrum (waveform)

	frequency bins specifies the number of frequency bins for which this VI computes the bispectrum. The resulting bispectrum S(f,f) is a square 2D array with the size (frequency bins/2+1). The default is 256.
	Xt specifies the input univariate time series.
	method specifies to compute the bispectrum with the fast Fourier transform (FFT) based or autoregressive (AR) model based method. The default is FFT. Refer to the Details section for more information about each method.
	window info specifies the information of the sliding window that divides the time series into subsequences. window specifies the time-domain window applied to the time series. Options include None (default), Hanning, Hamming, Blackman-Harris, Exact Blackman, Blackman, Flat Top, 4 Term B-Harris, 7 Term B-Harris, and Low Sidelobe. length specifies the length of the window. A large window generates a power spectral density (PSD) with small bias but results in a coarse PSD plot. A small window generates a smooth PSD plot but leads to large bias. The default is –1, which indicates that the window length equals the length of the input time series. overlap specifies the overlap, in percentage, of the moving window that this VI applies to the time series. This parameter determines how much data this VI reuses for the signal space matrix. A large overlap reduces the variance of the resulting power spectrum but increases computation time. The default is 50, which specifies that the overlap is half of the window length.
	error in describes error conditions that occur before this VI or function runs. The default is no error. If an error occurred before this VI or function runs, the VI or function passes the error in value to error out. This VI or function runs normally only if no error occurred before this VI or function runs. If an error occurs while this VI or function runs, it runs normally and sets its own error status in error out. Use the Simple Error Handler or General Error Handler VIs to display the description of the error code. Use error in and error out to check errors and to specify execution order by wiring error out from one node to error in of the next node. status is TRUE (X) if an error occurred before this VI or function ran or FALSE (checkmark) to indicate a warning or that no error occurred before this VI or function ran. The default is FALSE. code is the error or warning code. The default is 0. If status is TRUE, code is a nonzero error code. If status is FALSE, code is 0 or a warning code. source specifies the origin of the error or warning and is, in most cases, the name of the VI or function that produced the error or warning. The default is an empty string.
	dB on? specifies whether this VI returns the S(f,f) in decibels or in a linear scale. If dB on? is TRUE, this VI returns the S(f,f) in decibels. If dB on? is FALSE, this VI returns the S(f,f) in a linear scale. The default is TRUE.
	AR setting specifies the settings for the autoregressive (AR) model. This option is valid only when the method is AR Model. AR method specifies the method this VI uses to estimate the autoregressive (AR) model. 0 Forward-Backward (default)—Computes the AR coefficients by minimizing the least-square errors of the forward and backward predictions. 1 Least-Squares—Computes the AR coefficients by minimizing the least-square errors of the forward predictions. 2 Yule-Walker—Computes the AR coefficients by solving the Yule-Walker functions based on the forward predictions. 3 Burg-Lattice—Computes the AR coefficients using the Levinson-Durbin recursion based on the forward and backward predictions. The Levinson-Durbin recursion uses the arithmetic average. 4 Geometric-Lattice—Computes the AR coefficients using the Levinson-Durbin recursion based on the forward and backward predictions. The Levinson-Durbin recursion uses the geometric average. AR order specifies the order of the autoregressive (AR) model. The value of AR order must be greater than 0. The default is 4.
	S(f,f) returns the magnitude of the single-sided bispectrum S(f1, f2).
	freq bins returns the frequency bins at which this VI estimates the bispectrum.
	unit returns the engineering unit of the PSD. You can specify an engineering unit for a time series by using the TSA Scale to EU VI.
	error out contains error information. If error in indicates that an error occurred before this VI or function ran, error out contains the same error information. Otherwise, it describes the error status that this VI or function produces. Right-click the error out front panel indicator and select Explain Error from the shortcut menu for more information about the error. status is TRUE (X) if an error occurred or FALSE (checkmark) to indicate a warning or that no error occurred. code is the error or warning code. If status is TRUE, code is a nonzero error code. If status is FALSE, code is 0 or a warning code. source describes the origin of the error or warning and is, in most cases, the name of the VI or function that produced the error or warning.

TSA Bispectrum (array)

	sampling rate specifies the sampling rate, in hertz, of the input univariate time series Xt. The default is 1.
	frequency bins specifies the number of frequency bins for which this VI computes the bispectrum. The resulting bispectrum S(f,f) is a square 2D array with the size (frequency bins/2+1). The default is 256.
	Xt specifies the input univariate time series.
	method specifies to compute the bispectrum with the fast Fourier transform (FFT) based or autoregressive (AR) model based method. The default is FFT. Refer to the Details section for more information about each method.
	window info specifies the information of the sliding window that divides the time series into subsequences. window specifies the time-domain window applied to the time series. Options include None (default), Hanning, Hamming, Blackman-Harris, Exact Blackman, Blackman, Flat Top, 4 Term B-Harris, 7 Term B-Harris, and Low Sidelobe. length specifies the length of the window. A large window generates a power spectral density (PSD) with small bias but results in a coarse PSD plot. A small window generates a smooth PSD plot but leads to large bias. The default is –1, which indicates that the window length equals the length of the input time series. overlap specifies the overlap, in percentage, of the moving window that this VI applies to the time series. This parameter determines how much data this VI reuses for the signal space matrix. A large overlap reduces the variance of the resulting power spectrum but increases computation time. The default is 50, which specifies that the overlap is half of the window length.
	error in describes error conditions that occur before this VI or function runs. The default is no error. If an error occurred before this VI or function runs, the VI or function passes the error in value to error out. This VI or function runs normally only if no error occurred before this VI or function runs. If an error occurs while this VI or function runs, it runs normally and sets its own error status in error out. Use the Simple Error Handler or General Error Handler VIs to display the description of the error code. Use error in and error out to check errors and to specify execution order by wiring error out from one node to error in of the next node. status is TRUE (X) if an error occurred before this VI or function ran or FALSE (checkmark) to indicate a warning or that no error occurred before this VI or function ran. The default is FALSE. code is the error or warning code. The default is 0. If status is TRUE, code is a nonzero error code. If status is FALSE, code is 0 or a warning code. source specifies the origin of the error or warning and is, in most cases, the name of the VI or function that produced the error or warning. The default is an empty string.
	dB on? specifies whether this VI returns the S(f,f) in decibels or in a linear scale. If dB on? is TRUE, this VI returns the S(f,f) in decibels. If dB on? is FALSE, this VI returns the S(f,f) in a linear scale. The default is TRUE.
	AR setting specifies the settings for the autoregressive (AR) model. This option is valid only when the method is AR Model. AR method specifies the method this VI uses to estimate the autoregressive (AR) model. 0 Forward-Backward (default)—Computes the AR coefficients by minimizing the least-square errors of the forward and backward predictions. 1 Least-Squares—Computes the AR coefficients by minimizing the least-square errors of the forward predictions. 2 Yule-Walker—Computes the AR coefficients by solving the Yule-Walker functions based on the forward predictions. 3 Burg-Lattice—Computes the AR coefficients using the Levinson-Durbin recursion based on the forward and backward predictions. The Levinson-Durbin recursion uses the arithmetic average. 4 Geometric-Lattice—Computes the AR coefficients using the Levinson-Durbin recursion based on the forward and backward predictions. The Levinson-Durbin recursion uses the geometric average. AR order specifies the order of the autoregressive (AR) model. The value of AR order must be greater than 0. The default is 4.
	S(f,f) returns the magnitude of the single-sided bispectrum S(f1, f2).
	freq bins returns the frequency bins at which this VI estimates the bispectrum.
	error out contains error information. If error in indicates that an error occurred before this VI or function ran, error out contains the same error information. Otherwise, it describes the error status that this VI or function produces. Right-click the error out front panel indicator and select Explain Error from the shortcut menu for more information about the error. status is TRUE (X) if an error occurred or FALSE (checkmark) to indicate a warning or that no error occurred. code is the error or warning code. If status is TRUE, code is a nonzero error code. If status is FALSE, code is 0 or a warning code. source describes the origin of the error or warning and is, in most cases, the name of the VI or function that produced the error or warning.

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) = E[P(f₁)P(f₂)P*(f₁+f₂)]

E[X] denotes the expectation value of X. P(f) is the power spectral density of the time series X_t based on the TSA Periodogram VI.

where N is the number of frequency bins and f_s is the sampling rate. Before computing the bispectrum, this VI wraps X_t to an N-point series X_t'.

This VI computes the bispectrum of a univariate time series using the AR model based method according to the following equation:

S(f₁, f₂) = bP(f₁)P(f₂)P*(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, … ,a_n], 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.llb
• Beam Crack Detection VI: labview\examples\Time Series Analysis\TSAApplications.llb