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Owning Palette: Correlation and Spectral Analysis VIs

Installed With: Advanced Signal Processing Toolkit

Computes the single-sided power spectral density (PSD) of an input univariate time series based on autoregressive-moving average (ARMA) modeling. The PSD computed by this VI is exempt from window effects and has a better frequency resolution than the result from using the TSA Periodogram VI. This VI also matches the valleys in the spectrum better than the TSA AR Spectrum VI. Wire data to the Xt input to determine the polymorphic instance to use or manually select the instance.

Details  Example

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

Select an instance TSA ARMA Spectrum (waveform)TSA ARMA Spectrum (array)

TSA ARMA Spectrum (waveform)

	frequency bins specifies the number of frequency bins for which this VI computes the single-sided power spectral density PSD. The length of the single-sided PSD is (frequency bins/2+1). The default is 1024.
	Xt specifies the input univariate time series.
	method specifies the method to use in estimating the autoregressive-moving average model. 0 Yule-Walker (default)—Computes the AR coefficients and the MA coefficients separately with the extended Yule-Walker function based on the auto-correlation matrix. 1 High order AR—Computes the AR coefficients and the MA coefficients with a high-order AR model. 2 Polynomial—Computes the AR coefficients and the MA coefficients by solving the model-coefficient polynomial division.
	ARMA order specifies the order of the autoregressive-moving average model. AR specifies the AR order of the ARMA model. The value of AR must be greater than 0. The default is 4. MA specifies the MA order of the ARMA model. The value of MA must be greater than 0. The default is 1.
	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 PSD in decibels or in a linear scale. If dB on? is TRUE, this VI returns the PSD in decibels. If dB on? is FALSE, this VI returns the PSD in a linear scale. The default is TRUE.
	PSD returns information about the single-sided power spectral density (PSD). f0 returns the lower boundary, in hertz, of the frequency range. df returns the frequency increment, in hertz. S(f) returns the magnitude of the PSD at each frequency. The value of dB on? determines the unit of measurement for this parameter.
	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 ARMA Spectrum (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 single-sided power spectral density PSD. The length of the single-sided PSD is (frequency bins/2+1). The default is 1024.
	Xt specifies the input univariate time series.
	method specifies the method to use in estimating the autoregressive-moving average model. 0 Yule-Walker (default)—Computes the AR coefficients and the MA coefficients separately with the extended Yule-Walker function based on the auto-correlation matrix. 1 High order AR—Computes the AR coefficients and the MA coefficients with a high-order AR model. 2 Polynomial—Computes the AR coefficients and the MA coefficients by solving the model-coefficient polynomial division.
	ARMA order specifies the order of the autoregressive-moving average model. AR specifies the AR order of the ARMA model. The value of AR must be greater than 0. The default is 4. MA specifies the MA order of the ARMA model. The value of MA must be greater than 0. The default is 1.
	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 PSD in decibels or in a linear scale. If dB on? is TRUE, this VI returns the PSD in decibels. If dB on? is FALSE, this VI returns the PSD in a linear scale. The default is TRUE.
	PSD returns information about the single-sided power spectral density (PSD). f0 returns the lower boundary, in hertz, of the frequency range. df returns the frequency increment, in hertz. S(f) returns the magnitude of the PSD at each frequency. The value of dB on? determines the unit of measurement for this parameter.
	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 ARMA Spectrum Details

This VI computes the PSD of a univariate time series based on autoregressive-moving average (ARMA) modeling according to the following equation:

where S(f) is the PSD of the time series, df is the frequency interval, which is computed as f_s/N. N is the number of frequency bins, f_s is the sampling rate, and s² is the estimated noise series of the ARMA model of the time series. a is an array that contains the AR coefficients of the ARMA(m, n) model, and a=[1, a₁, a₂,…, a_m]. b is another array that contains the MA coefficients of the ARMA(m, n) model, and b=[1, b₁, b₂,…, b_n]. Before computing the PSD, this VI wraps a, b to N-point series a', b'.

The minimum length requirement for the input time series differs for each method you use:

• Yule-Walker method: minimum length ≥ AR order + MA order
• High-Order AR method: minimum length ≥ 5 × MA order
• Polynomial method: minimum length ≥ 5 × (AR order + MA order)

Example

Refer to the Power Spectral Density Estimation VI in the labview\examples\Time Series Analysis\TSAGettingStarted.llb for an example of using the TSA ARMA Spectrum VI.