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

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Equivalent Prediction Filter Representation

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

More About

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Algorithms

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].

References

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

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