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.

Example

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

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

3. Implements a = [1 a]

See Also

ac2poly	Convert an autocorrelation sequence to a prediction filter polynomial.
latc2tf	Lattice filter to transfer function conversion.
latcfilt	Lattice and lattice-ladder filter implementation.
poly2rc	Convert a prediction filter polynomial to reflection coefficients.
rc2ac	Convert reflection coefficients to an autocorrelation sequence.
rc2is	Convert reflection coefficients to inverse sine parameters.
rc2lar	Convert reflection coefficients to log area ratio parameters.
tf2latc	Convert transfer function to lattice filter.

References

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

rc2lar

rceps