aryule {gsignal}

Autoregressive model coefficients - Yule-Walker method

Description

compute autoregressive all-pole model parameters using the Yule-Walker method.

Usage

aryule(x, p)

Arguments

x

input data, specified as a numeric or complex vector or matrix. In case of a vector it represents a single signal; in case of a matrix each column is a signal.

p

model order; number of poles in the AR model or limit to the number of poles if a valid criterion is provided. Must be smaller than the length of x minus 1.

Details

aryule uses the Levinson-Durbin recursion on the biased estimate of the sample autocorrelation sequence to compute the parameters.

Value

A list containing the following elements:

a

vector or matrix containing (p + 1) autoregression coefficients. If x is a matrix, then each row of a corresponds to a column of x. a has p + 1 columns.

e

white noise input variance, returned as a vector. If x is a matrix, then each element of e corresponds to a column of x.

k

Reflection coefficients defining the lattice-filter embodiment of the model returned as vector or a matrix. If x is a matrix, then each column of k corresponds to a column of x. k has p rows.

Note

The power spectrum of the resulting filter can be plotted with pyulear(x, p), or you can plot it directly with ar_psd(a,v,...).

Author(s)

Paul Kienzle, [e-mail],
Peter V. Lanspeary, [e-mail].
Conversion to R by Geert van Boxtel, [e-mail].

See Also

ar_psd, arburg

Examples

a <- Arma(1, c(1, -2.7607, 3.8106, -2.6535, 0.9238))
y <- filter(a, rnorm(1024))
coefs <- aryule(y, 4)