optic.dsp.core.levinson

levinson(r, nTaps)

Levinson-Durbin algorithm

Parameters:

• r (array-like) – Autocorrelation coefficients of the signal, where r[0] is the zero-lag autocorrelation and r[k] is the autocorrelation at lag k.

• nTaps (int) – The order of the whitening filter (number of coefficients to estimate).

Returns:

a – The coefficients of the whitening filter of length nTaps, where a[0] is the leading coefficient (usually 1) and a[1], a[2], …, a[nTaps-1] are the estimated filter coefficients.

Return type:

np.ndarray

Notes

The Levinson-Durbin algorithm is an efficient method for solving the Toeplitz system of equations that arises in linear prediction and filter design. The resulting coefficients can be used to design a whitening filter that decorrelates the input signal.

References

[1] Levinson, N., The Wiener RMS error criterion in filter design. Journal of Mathematics and Physics, 25(1-4), 261-278, 1947.

[2] Durbin, J., The fitting of time-series models. Review of the International Statistical Institute, 28(3), 233-244, 1960.