9 init_ outerr

Purpose

Creates and initializes the variables required for the Output Error recursive adaptive algorithm. The filter transfer function is given by

$$w(z) = \frac{A(z)}{1-B(z)}$$ (67)

where

$$A(z) = a_0 + a_1 z^{-1} + ... + a_{N-1} z^{-N+1}$$ (68)

$$B(z) = b_1 z^{-1} + b_2 z^{-2} + ... + b_M z^{-M}$$ (69)

Syntax

[u,w,c,y,d,e,mu,Px,Py]=init_outerr(N,M)
[u,w,c,y,d,e,mu,Px,Py]=init_outerr(N,M,u0,w0,c0,d0,mu0)

Description

The variables of the output error algorithm are summarized below (see Fig. 6.5).

Input arguments:
   N   : Number of coefficients of A(z).
   M   : Number of coefficients of B(z).
   u0  : composite input vector [N+M x 1]
   w0  : composite filter coefficients vector
   c0  : composite gradient vector
   d0  : initial desired sample
   mu0 : vector of step sizes
Output Parameters [default]:
   u   : initialized composite input [zeros]
   w   : initialized filter coef. vector [zeros]
   c   : initialized gradient vector [zeros]
   y   : filter output [zeros]
   d   : Initialized desired signal [white noise]
   e   : Initial error signal [e=d-y]
   mu  : step size vector [.01 ... .01)].
   Px  : power of x(n).
   Py  : power of y(n).

Example

N  = 2;                   % Number of numerator coef. 
M  = 2;                   % Number of denumerator coef. 
w0 = [1;0;0;0];           % initial filter coef. 
u0 = rand(4,1);           % initial composite input vector
c0 = zeros(4,1);          % initial gradient vector
d0 = 0;                   % desired sample
mu = [0.1;0.1;0.01;0.01]; % step size vector
% Create and initialize an Output Error filter
[u,w,c,y,d,e,mu,Px,Py]=init_outerr(N,M,u0,w0,c0,d0,mu);

Remarks

• Supports both real and complex signals and filters.
• Use input parameters 3 through 7 to initialize the algorithm storage. This is helpful when the adaptation process is required to start from a known operation point calculated off-line or from previous simulations.

See Also

ASPTOUTERR, MODEL_ OUTERR.