Signal Processing Toolbox

rc2poly

Convert reflection coefficients to a 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:

1. Sets the output vector a to the first element of k
2. Loops through the remaining elements of k

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

3. Implements a = [1 a]

See Also

ac2poly, latc2tf, latcfilt, poly2rc, rc2ac, rc2is, rc2lar, tf2latc

References

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

rc2lar

rceps