Learn more about Signal Processing Toolbox

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

Consider a lattice IIR filter given by reflection coefficients k:

k = [0.3090    0.9800    0.0031    0.0082   -0.0082];

Its equivalent prediction filter representation is given by

a = rc2poly(k)
a =
    1.0000   0.6148   0.9899   0.0000   0.0032  -0.0082

Algorithm

rc2poly computes output a using Levinson's recursion [1]. The function

Sets the output vector a to the first element of k.
Loops through the remaining elements of k.
For each loop iteration i, a = [a + a(i-1:-1:1)*k(i) k(i)].
Implements a = [1 a].

References

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