gsignal (version 0.3-1)

arburg: Autoregressive model coefficients - Burg's method

Description

Calculate the coefficients of an autoregressive model using the whitening lattice-filter method of Burg (1968)[1].

Usage

arburg(x, p, criterion = NULL)

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 < length(x) - 2.

criterion

model-selection criterion. Limits the number of poles so that spurious poles are not added when the whitened data has no more information in it. Recognized values are:

AKICc

approximate corrected Kullback information criterion (recommended)

KIC

Kullback information criterion

AICc

corrected Akaike information criterion

AIC

Akaike information criterion

FPE

final prediction error

The default is to NOT use a model-selection criterion (NULL)

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.

Details

The inverse of the autoregressive model is a moving-average filter which reduces x to white noise. The power spectrum of the AR model is an estimate of the maximum entropy power spectrum of the data. The function ar_psd calculates the power spectrum of the AR model.

For data input x(n) and white noise e(n), the autoregressive model is

                          p+1
    x(n) = sqrt(v).e(n) + SUM a(k).x(n-k)
                          k=1
 

arburg does not remove the mean from the data. You should remove the mean from the data if you want a power spectrum. A non-zero mean can produce large errors in a power-spectrum estimate. See detrend

References

[1] Burg, J.P. (1968) A new analysis technique for time series data, NATO advanced study Institute on Signal Processing with Emphasis on Underwater Acoustics, Enschede, Netherlands, Aug. 12-23, 1968. [2] Seghouane, A. and Bekara, M. (2004). A small sample model selection criterion based on Kullback<U+2019>s symmetric divergence. IEEE Trans. Sign. Proc., 52(12), pp 3314-3323,

See Also

ar_psd

Examples

# NOT RUN {
A <- Arma(1, c(1, -2.7607, 3.8106, -2.6535, 0.9238))
y <- filter(A, 0.2 * rnorm(1024))
coefs <- arburg(y, 4)

# }