levinson {signal}

Durbin-Levinson Recursion

Description

Perform Durbin-Levinson recursion on a vector or matrix.

Usage

levinson(x, p = NULL)

Arguments

x

Input signal.

p

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

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.

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.

Author(s)

Original Octave version by Paul Kienzle [e-mail] based on yulewalker.m by Friedrich Leisch [e-mail]. Conversion to R by Sebastian Krey [e-mail].

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/