poly2ac

Transformation of the predictive filter polynomial into an autocorrelation sequence.

Library

EngeeDSP

Syntax

ac = poly2ac(a,eFinal) — returns a vector ac, approximately equal to the autocorrelation sequence, from the polynomial of the autoregressive predictive filter a and the final prediction error eFinal.

# a — coefficients of the predictive filter

+ vector

Details

Coefficients of the predictive filter, specified as a vector.

The value of the argument a It has the following limitations:

a[1] can’t be equal to 0;
If a[1] not equal to 1, function poly2ac normalizes the polynomial of the predictive filter to a[1].

Типы данных	`Float32`, `Float64`
Support for complex numbers	Yes

# eFinal — power of finite prediction error

+ scalar

Details

The power of the finite prediction error, given as a scalar.

Типы данных	`Float32`, `Float64`
Support for complex numbers	Yes

# ac — autocorrelation sequence

+ vector

Details

An autocorrelation sequence returned as a column vector with the same number of elements as in the vector a.

Details

Let be given a polynomial a predictive filter and the final prediction error efinal, we find the autocorrelation sequence.

import EngeeDSP.Functions: poly2ac

a = [1.0000 0.6147 0.9898 0.0004 0.0034 -0.0077]
efinal = 0.2
ac = poly2ac(a, efinal)

6-element Vector{Float64}:
  5.591709093839243
 -1.7276920029304619
 -4.423063394533152
  4.398506494154623
  1.6425622434116223
 -5.312625200749032

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