# 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 polynomial represents the coefficients of a prediction filter that outputs a signal with autocorrelation sequence approximately equal to r.

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

## Examples

collapse all

Given an autocorrelation sequence, r, determine the equivalent linear prediction filter polynomial and the final prediction error.

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

[a,efinal] = ac2poly(r)
a = 1×6

1.0000    0.6147    0.9898    0.0004    0.0034   -0.0077

efinal = 0.1791

## Tips

You can apply this function to real or complex data.

## References

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

## Version History

Introduced before R2006a