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levinson

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 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.

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

signal

Signal Processing

v0.7-6
GPL-2
Authors
Uwe Ligges [aut, cre] (new maintainer), Tom Short [aut] (port to R), Paul Kienzle [aut] (majority of the original sources), Sarah Schnackenberg [ctb] (various test cases and bug fixes), David Billinghurst [ctb], Hans-Werner Borchers [ctb], Andre Carezia [ctb], Pascal Dupuis [ctb], John W. Eaton [ctb], E. Farhi [ctb], Kai Habel [ctb], Kurt Hornik [ctb], Sebastian Krey [ctb], Bill Lash [ctb], Friedrich Leisch [ctb], Olaf Mersmann [ctb], Paulo Neis [ctb], Jaakko Ruohio [ctb], Julius O. Smith III [ctb], Doug Stewart [ctb], Andreas Weingessel [ctb]
Initial release
2015-07-29

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