21 model_ arlmsnewt

Purpose

Simulation of an adaptive forward modeling application using an adaptive transversal filter updated with the autoregressive modeling version of the LMS-Newton algorithm.

Syntax

model_arlmsnewt

Description

Figure 10.41: Block diagram of a forward modeling application using the autoregressive LMS-Newton algorithm.

The block diagram of the system identification (forward modeling) problem using the autoregressive LMS-Newton adaptive algorithm is shown in Fig. 10.41, (see Section 4.1 for more details on the ARLMSNEWT algorithm). The input signal $x(n)$ (measured signal at the input of the system to be modeled) is stored in the file infile. The desired signal $d(n)$ (the signal measured at the system output in response to applying $x(n)$ at its input) is stored in the file dfile. First the variables for the LMS-Newton algorithm are creates and initializes using init_arlmsnewt(), and the input signals are read from files, then a processing loop is started. In each iteration of the loop asptarlmsnewt() is called with a new input sample and a new desired sample to calculate the filter output (estimated desired signal) and update the adaptive model coefficients. This simulation script uses the standard ASPT iteration progress window (IPWIN). The IPWIN has four buttons which allow you to stop and continue the simulation, show or hide the simulation graph window, break out of the processing loop, and quit the simulation. After processing all the samples, or on pressing the break or stop buttons, the sensor signal $e(n)$ is written to a wave audio file and a graph presenting the echo canceler performance is generated.

Code

clear all;
load .\data\h512;                % for verification

% Data files
infile = '.\wavin\scinwn.wav';   % input signal, white noise
dfile  = '.\wavin\scdwn512.wav'; % system output 

% Simulation parameters
L      = 512;                    % adaptive model length
M      = 3;                      % AR model coef. 
mu_w   = .4/L;                   % FIR filter step size
mu_p   = 1e-6;                   % lattice predictor step size
maxk   = .99;                    % maximum value for PARCOR

%% Initialize storage 
[k,w,x,b,u,P,d,y,e] = init_arlmsnewt(L,M); % Init LMS Newton 				
[xn,inFs,inBits] = wavread(infile);    % read input signal
[dn,inFs,dBits]  = wavread(dfile);     % read desired signal
inSize  = min(length(dn),length(xn));  % samples to process
E       = init_ipwin(inSize);          % Initialize IPWIN

%% Processing Loop
for (m=1:inSize)
   x  = [xn(m,:);x(1:end-1,:) ];     % update the delay line
   d  = dn(m);                       % new desired sample

   % update the adaptive model
   [k,w,b,u,P,y,e] = asptarlmsnewt(k,w,x,b,u,P,d,mu_p,mu_w,maxk);

   % update the iteration progress window
   [E, stop,brk] = update_ipwin(E,e,d,'m',w,h512);

   % handle the Stop button
   while (stop ~= 0), stop = getStop; end;

   % handle the Break button		
   if (brk), plot_model(w,h512,E); break; end;	
end;

plot_model(w,h512,E);

Results

Figure 10.42: Performance of the autoregressive LMS-Newton adaptive filter in a system identification application.

Running the above script will produce the graph shown in Fig. 10.42. The two top-left panels in Fig. 10.42 show the time and frequency responses of the unknown system for which this application is intended to provide a FIR model. The time and frequency responses for the model obtained by the adaptive filter are shown in the two top-right panels. The bottom-left panel shows the learning curve and the bottom-right panel shows the error in the filter coefficients by the end of the simulation.

See Also

INIT_ ARLMSNEWT, ASPTARLMSNEWT.

Reference

[2] and [4] for analysis of the adaptive Lattice filters, [2] and [11] for analysis of the LMS-Newton algorithm.