8 init_ sovrls

Purpose

Creates and initializes the variables required for the Second Order Volterra Recursive Least Squares (RLS) Adaptive Filter.

Syntax

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

Description

The second order Volterra RLS 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 RLS filter. The variables of the SOVRLS 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
  b  : a small +ve constant to initialize R 
  w0 : initial coefficients 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 [y = w' * x]
  e  : Initialized error sample [e = d - y]
  R  : Initialized inverse of the weighted 
       auto correlation matrix of x, [R=b*eye(L1 + sum(1:L2))]

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 SOVRLS FIR filter
[w,x,d,y,e,R]=init_sovrls(L1,L2,.01,w0,x0,d0);

Remarks

• Supports both real and complex signals and filters.
• Use input parameters 4 through 6 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

ASPTSOVRLS.