Computes the single-sided power spectral density (PSD) of a 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.


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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 fs/N. N is the number of frequency bins, fs 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,…, am]. b is another array that contains the MA coefficients of the ARMA(m, n) model, and b=[1, b1, b2,…, bn]. 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 x MA order
  • Polynomial method: minimum length >= 5 x (AR order + MA order)

Examples

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