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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 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 = 1.0000 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.