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.


icon

Inputs/Outputs

  • cdbl.png sampling rate —

    sampling rate specifies the sampling rate, in hertz, of the univariate time series Xt. The default is 1.

  • ci32.png frequency bins —

    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.

  • c1ddbl.png Xt —

    Xt specifies the univariate time series.

  • cu16.png method —

    method specifies the method to use in estimating the autoregressive-moving average model.

  • cnclst.png ARMA order —

    ARMA order specifies the order of the autoregressive-moving average model.

  • ci32.png AR —

    AR specifies the AR order of the ARMA model. The value of AR must be greater than 0. The default is 4.

  • ci32.png MA —

    MA specifies the MA order of the ARMA model. The value of MA must be greater than 0. The default is 1.

  • cerrcodeclst.png error in (no error) —

    error in describes error conditions that occur before this node runs. This input provides standard error in functionality.

  • cbool.png dB on? (T) —

    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.

  • icclst.png PSD —

    PSD returns information about the single-sided power spectral density (PSD).

  • idbl.png f0 —

    f0 returns the lower boundary, in hertz, of the frequency range.

  • idbl.png df —

    df returns the frequency increment, in hertz.

  • i1ddbl.png S(f) —

    S(f) returns the magnitude of the PSD at each frequency. The value of dB on? determines the unit of measurement for this parameter.

  • ierrcodeclst.png error out —

    error out contains error information. This output provides standard error out functionality.

    • 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.