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signal (version 1.8-0)

levinson: Durbin-Levinson Recursion

Description

Perform Durbin-Levinson recursion on a vector or matrix.

Usage

levinson(x, p = NULL)

Value

a

The denominator filter coefficients.

v

Variance of the white noise = square of the numerator constant.

ref

Reflection coefficients = coefficients of the lattice implementation of the filter.

Arguments

x

Input signal.

p

Lag (defaults to length(x) or nrow(x)).

Author

Original Octave version by Paul Kienzle pkienzle@users.sf.net based on yulewalker.m by Friedrich Leisch Friedrich.Leisch@boku.ac.at. Conversion to R by Sebastian Krey krey@statistik.tu-dortmund.de.

Details

Use the Durbin-Levinson algorithm to solve:

toeplitz(acf(1:p)) * y = -acf(2:p+1).

The solution [1, y'] is the denominator of an all pole filter approximation to the signal x which generated the autocorrelation function acf.

acf is the autocorrelation function for lags 0 to p.

References

Steven M. Kay and Stanley Lawrence Marple Jr.: Spectrum analysis -- a modern perspective, Proceedings of the IEEE, Vol 69, pp 1380-1419, Nov., 1981

Octave https://octave.sourceforge.io/