8 init_ eqerr

Purpose

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

$$w(z) = \frac{A(z)}{1-B(z)}$$ (64)

where

$$A(z) = a_0 + a_1 z^{-1} + ... + a_{N-1} z^{-N+1}$$ (65)

$$B(z) = b_1 z^{-1} + b_2 z^{-2} + ... + b_M z^{-M}$$ (66)

Syntax

[u,w,y,e,mu,Px,Pd] = init_eqerr(N,M)
[u,w,y,e,mu,Px,Pd] = init_eqerr(N,M,u0,w0,y0,d0,mu0)

Description

The variables of the equation error algorithm are summarized below (see Fig. 6.3).

Input Parameters:
   N   : Number of coefficients of A(z)
   M   : Number of coefficients of B(z)
   u0  : [x(0) x(-1) ... x(-N+1) d(0) ... d(-M)]' 
   w0  : [a_0 a_1 ... a_(N-1) b_1 ... b_M]'
   y0  : [y(-1) y(-2) ... y(-M)]' 
   d0  : desired signal at time index 0
   mu0 : vector of step sizes 
Output Parameters [default]:
   u   : initialized composite input [zeros]
   w   : initialized filter coef. [zeros]
   y   : initialized filter output vector [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).
   Pd  : power of d(n).

Example

N  = 2;                   % Number of numerator coef. 
M  = 2;                   % Number of denumerator coef. 
u0 = rand(4,1);           % initial composite input vector
y0 = zeros(2,1);          % initial output 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,y,e,mu,Px,Pd]=init_eqerr(N,M,u0,[],y0,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

ASPTEQERR, MODEL_ EQERR.