28 model_ tdlms

Purpose

Simulation of an adaptive forward modeling application using a transversal adaptive filter updated according to the Transform Domain LMS adaptive algorithm.

Syntax

model_tdlms

Description

Figure 10.55: Block diagram of an FIR forward modeling using the TDLMS adaptive algorithm.

The block diagram of the system identification (forward modeling) problem using the TDLMS adaptive algorithm is shown in Fig. 10.55. The simulation uses a transversal FIR filter for the adjustable filter and the coefficients of the filter are updated using the TDLMS 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 adaptive model $\vW (n)$ are created and initialized using init_tdlms(), and the input signals are read from files, then a processing loop is started. In each iteration of the loop aspttdlms() is called with a new input sample and a new desired sample to calculate the filter output (estimated desired signal) and update the filter 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
infile = '.\wavin\scinwn.wav';      % input signal, white noise
dfile  = '.\wavin\scdwn512.wav';    % system output 

L      = 512;                       % adaptive model length
mu     = 0.5/L;                     % Step size
b      = 0.98;                      % pole for power estimation
T      = 'fft';                     % Transform type

%% Initialize storage 
[W,w,x,d,y,e,p]  = init_tdlms(L);   % Initialize TDLMS algorithm				
[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:L-1,:) ]; % update the input delay line
   d  = dn(m);                % get the new desired sample
   [W,y,e,p,w] = aspttdlms(x,W,d,mu,p,b,T);

   % 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 10.56: Performance of the Transform Domain LMS (TDLMS) adaptive filter in a system identification application.

Running the above script will produce the graph shown in Fig. 10.56. The two top-left panels in Fig. 10.56 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_ TDLMS, ASPTTDLMS.

Reference

[11], [2], and [4] for extensive analysis of the LMS and the steepest-descent search method.