tuneR (version 0.4-1)

levinson: Durbin-Levinson Recursion

Description

Internal: Perform Durbin-Levinson recursion on vector or matrix.

Usage

levinson(x, p = NULL)

Arguments

x

Input signal.

p

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

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.

concept

• levinson
• durbin
• recursion

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

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