rc2poly (Signal Processing Toolbox)

Conversion of reflection coefficients to prediction polynomial.

Syntax

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

Description

a = rc2poly(k)

finds the prediction polynomial a, with a(1) = 1, from the reflection coefficients k of the corresponding lattice structure. Output a is row vector of length k + 1.

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

returns the final prediction error, efinal, based on the zero-lag autocorrelation, r0.

Example

Consider an IIR filter given by reflection coefficients k:

k = [0.3090    0.9800    0.0031    0.0082   -0.0082];

Its polynomial representation is

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.: Implementsa = [1 a]

See Also


`ac2poly`	Conversion of autocorrelation sequence to prediction polynomial.
`latc2tf`	Lattice filter to transfer function conversion.
`latcfilt`	Lattice and lattice-ladder filter implementation.
`poly2rc`	Conversion of prediction polynomial to reflection coefficients.
`rc2ac`	Conversion of reflection coefficients to autocorrelation sequence.
`tf2latc`	Conversion of transfer function to lattice filter.

References

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

[ Previous | Help Desk | Next ]