This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materials including this page, select Japan from the country navigator on the bottom of this page.


Convert reflection coefficients to prediction filter polynomial


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


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.


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 = 

    1.0000    0.6148    0.9899    0.0000    0.0032   -0.0082


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


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

Introduced before R2006a

Was this topic helpful?