9 init_ ftrls

Purpose

Creates and initializes the variables required for the Fast Transversal Recursive Least Squares algorithm.

Syntax

[ff,bb,k,cf,c,g,w,x,d,e,y] = init_ftrls(L)
[ff,bb,k,cf,c,g,w,x,d,e,y] =
init_ftrls(L,ff0,bb0,k0,cf0,c0,g0,w0,x0,d0)

Description

The variables of the FTRLS algorithm are summarized below.

Input Parameters [Size]:: 
  L   : Linear combiner length
  ff0 : initial autocorrelation of forward prediction error [1x1]
  bb0 : initial autocorrelation of backward prediction error [1x1]
  k0  : initial normalized gain vector [Lx1]
  cf0 : initial conversion factor [1x1]
  c0  : initial forward predictor coefficients [L+1 x 1]
  g0  : initial backward predictor coefficients [L+1 x 1]
  w0  : initial linear combiner coefficients [L x 1]
  x0  : initial input samples vector [L+1 x 1]
  d0  : initial desired response [1x1]

Output parameters [Default]::
  ff  : autocorrelation of forward prediction error [.001]
  bb  : autocorrelation of backward prediction error [.001]
  k   : normalized gain vector [ones].
  cf  : conversion factor [1]
  c   : forward predictor coefficients [.1*ones(L+1,1)]
  g   : backward predictor coefficients [.1*ones(L+1,1)]
  w   : linear combiner coefficients [zeros]
  x   : input samples vector [zeros]
  d   : desired output [rand]
  y   : Linear combiner output [w' * x(1:end-1)]
  e   : Linear combiner error [d-y]

Example

L  = 5;                 % Number of lattice stages 
ff = 0.01;              % autocorr. of forward prediction error
bb = 0.01;              % autocorr. of backward prediction error
k  = zeros(L,1);        % normalized gain vector
cf = 1;                 % conversion factor
c  = .01*ones(L+1,1);   % forward prediction coef. vector
g  = zeros(L+1,1);      % backward prediction coef. vector 
w  = zeros(L,1);        % linear combiner coef. vector

% Create and initialize an RLS lattice filter
[ff,bb,k,cf,c,g,w,x,d,e,y]=init_ftrls(L,ff,bb,k,cf,c,g,w,[],0);

Remarks

• Supports both real and complex signals and filters.
• Use input parameters 2 through 9 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 and is also used for soft initialization when instability signs are detected.

See Also

ASPTFTRLS, ASPTRLSLATTICE2.