10 init_ sovvsslms

Purpose

Creates and initializes the variables required for the Second Order Volterra Variable Step Size Least Mean Squares adaptive algorithm.

Syntax

[w,x,d,y,e,g,mu] = init_sovvsslms(L1,L2)
[w,x,d,y,e,g,mu] = init_sovvsslms(L1,L2,w0,x0,d0,mu0,g0)

Description

The second order Volterra VSSLMS filter consists of a linear filter part of length L1 and a nonlinear filter part. The nonlinear part uses the combination of cross-products between samples in the delay line. The number of past samples used in the nonlinear part is defined by the L2 parameter. A value of L2=0 reduces the Volterra filter to a linear VSSLMS filter. The variables of the SOVVSSLMS are summarized below.

Input Parameters [Size] :: 
  L1  : memory length of the linear part of the filter
  L2  : memory length of the non-linear part of the filter
  w0  : initial coefficient vector [L1 + sum(1:L2) x 1] 
  x0  : initial input samples vector [L1 + sum(1:L2) x 1] 
  d0  : initial desired sample [1 x 1] 
  mu0 : initial step-size vector [L1 + sum(1:L2) x 1]
  g0  : initial gradient vector [L1 + sum(1:L2) x 1]

Output parameters [default] ::
  w   : initialized filter coefficients [zeros]
  x   : initialized input vector [zeros]
  d   : initialized desired sample [white noise]
  y   : Initialized filter output 
  e   : initialized error sample [e = d - y]
  g   : initialized gradient vector [zeros]
  mu  : initialized step-size vector [zeros]

Example

L1 = 3;              % Memory of linear filter
L2 = 2;              % Memory of nonlinear filter 
W0 = zeros(6,1);     % initial filter coefficients 
x0 = rand(6,1);      % initial delay line
d0 = 0;              % desired sample
mu0= .001*ones(6,1); % initial step sizes

% Create and initialize a SOVTDLMS FIR filter
[w,x,d,y,e,g,mu]=init_sovvsslms(L1,L2,w0,x0,d0,mu0);

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

ASPTSOVVSSLMS.