6 init_ sovlms

Purpose

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

Syntax

[w,x,d,y,e] = init_sovlms(L1,L2)
[w,x,d,y,e] = init_sovlms(L1,L2,w0,x0,d0)

Description

The second order Volterra LMS 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 LMS filter. The variables of the SOVLMS are summarized below.

Input Parameters [Size] :: 
  L1 : memory length of the linear part of the filter
  L2 : memory length of the nonlinear 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] 
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]

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

% Create and initialize a SOVLMS FIR filter
[w,x,d,y,e]=init_sovlms(L1,L2,w0,x0,d0);

Remarks

• Supports both real and complex signals and filters.
• Use input parameters 3 through 5 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

ASPTSOVLMS.