ac2rc

Transformation of the autocorrelation sequence into reflection coefficients.

Library

EngeeDSP

Syntax

Function call

k,r0 = ac2rc(ac) — returns reflection coefficients k obtained from the autocorrelation sequence ac. Function ac2rc also returns zero-delay autocorrelation r0.

Arguments

Input arguments

# ac — autocorrelation sequence

+ vector | the matrix

Details

An autocorrelation sequence given as a vector or matrix. Function ac2rc considers each column ac as a separate channel.

Data types	`Float64`
Support for complex numbers	Yes

Output arguments

# k — reflection coefficients

+ vector | the matrix

Details

A list of reflection coefficients returned as a column vector or matrix. This list has as many columns (channels) as the argument ac, and lines where — number of rows of the matrix ac.

# r0 — zero-delay autocorrelation

+ scalar | vector

Details

Zero-delay autocorrelation, returned as a scalar or column vector with as many rows as the number of channels (columns) the argument has ac.

Examples

Reflection coefficients obtained from the autocorrelation sequence

Details

Let an autocorrelation sequence be given ac, we determine the reflection coefficients of the corresponding lattice structure and the zero-delay autocorrelation.

import EngeeDSP.Functions: ac2rc

ac = [5.0000 -1.5450 -3.9547 3.9331 1.4681 -4.7500]'

k, r0 = ac2rc(ac)

println("k = ", k, "\nr0 = ", r0)

k = [0.309; 0.979991575633016; 0.0030208486681116194; 0.00818464674072109; -0.007709673467442522;;]
r0 = 5.0

Tips

Reflection coefficients can be used k to find a predictive filter of a lattice structure that creates a sequence with approximately the same autocorrelation sequence as the given sequence ac. For more information, see the function description rc2poly.

Literature

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