# rc2poly

Convert reflection coefficients to prediction filter polynomial

## Syntax

```a = rc2poly(k) [a,efinal] = rc2poly(k,r0) ```

## Description

`a = rc2poly(k)` converts the reflection coefficients `k` corresponding to the lattice structure to the prediction filter polynomial `a`, with `a(1)` = `1`. The output `a` is row vector of length `length(k)` + 1.

`[a,efinal] = rc2poly(k,r0)` returns the final prediction error `efinal` based on the zero-lag autocorrelation, `r0`.

## Examples

collapse all

Consider a lattice IIR filter given by a set of reflection coefficients. Find its equivalent prediction filter representation.

```k = [0.3090 0.9800 0.0031 0.0082 -0.0082]; a = rc2poly(k)```
```a = 1×6 1.0000 0.6148 0.9899 0.0000 0.0032 -0.0082 ```

## Algorithms

`rc2poly` computes output `a` using Levinson's recursion . The function

1. Sets the output vector `a` to the first element of `k`.

2. Loops through the remaining elements of `k`.

For each loop iteration `i`, ```a = [a + a(i-1:-1:1)*k(i) k(i)]```.

3. Implements` a = [1 a]`.

## References

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