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ac2poly - Convert autocorrelation sequence to prediction polynomial

Syntax

a = ac2poly(r) [a,efinal] = ac2poly(r)

Description

a = ac2poly(r) finds the linear prediction, FIR filter polynomial a corresponding to the autocorrelation sequence r. a is the same length as r, and a(1) = 1. The prediction filter polynomial represents the coefficients of the prediction filter whose output produces a signal whose autocorrelation sequence is approximately the same as the given autocorrelation sequence r.

[a,efinal] = ac2poly(r) returns the final prediction error efinal, determined by running the filter for length(r) steps.

Remarks

You can apply this function to real or complex data.

Examples

Consider the autocorrelation sequence:

r = [5.0000 -1.5450 -3.9547 3.9331 1.4681 -4.7500];

The corresponding prediction filter polynomial is

[a,efinal] = ac2poly(r)
a =
    1.0000  0.6147  0.9898  0.0004  0.0034 -0.0077
efinal =
    0.1791

References

[1] Kay, S.M. Modern Spectral Estimation. Englewood Cliffs, NJ: Prentice-Hall, 1988.