Weights of LMS adaptives filter: bode commant, plot magnitude and phase

Hello, I would like to know if there is a way to plot the magnitude and the phase of the values of the weights returned by LMS adapative filter.

By the way: is there any way to convert this filter to transfer function?

w =

   -0.1229
   -0.0786
   -0.0391
   -0.0043
    0.0284
    0.0594
    0.0913
    0.1247
    0.1620
    0.2035
    0.2515

Answer 1

[Dimitris Kalogiros]

A very useful script for your case:

clear; clc; close all;

% LMS weights
w=[ -0.1229   -0.0786   -0.0391     -0.0043    0.0284      0.0594...
     0.0913    0.1247    0.1620      0.2035    0.2515                ];

%sampling period of our system;
Ts=1;

% LMS feedforward is a filter
sys=tf(w, 1, Ts, 'variable','z^-1');

% plot bode diagram
figure;
bode(sys);
grid on; zoom on;

If you run the script, you will receive bode diagram:

[Eloy Pena Asensio]

Thank you very much! What about my second question?

Is there any way to transform transfer function into a filter?

[Dimitris Kalogiros]

Mapping transfer function to filter coefficients is not an easy task, but it is feasible. If I find some time , later on night I will give you an example

Answer 2

[Dimitris Kalogiros]

Here you are a more complete script:

clear; clc; close all;

%%problem definition
% LMS weights
w=[ -0.1229   -0.0786   -0.0391     -0.0043    0.0284      0.0594...
     0.0913    0.1247    0.1620      0.2035    0.2515                ];

%sampling period of out system;
Ts=1;

%%analyse LMS taps
% magnitude and phase of taps
tap.magn=abs(w);
tap.phase=atan2(imag(w),real(w));
figure; 
subplot(2,2,1); stem(tap.magn, '-b*'); title('magnitude of taps');
ylabel('magnitude'); xlabel('tap number'); zoom on; grid on;
subplot(2,2,2); plot(log10(tap.magn), '-b.'); title('magnitude of taps expressed at dB');
ylabel('dB'); xlabel('tap number'); zoom on; grid on;
subplot(2,1,2); plot(tap.phase, '-ro'); title('phase of taps');
xlabel('rand'); ylabel('tap number'); zoom on; grid on;

% LMS feedforward is a filter. Find its frequency response
sys=tf(w, 1, Ts, 'variable','z^-1');

% plot bode diagram
figure;
bode(sys);
grid on; zoom on;

Keep in mind that your LMS coefficients are real numbers, so seeking "magnitude" and "phase" of these values is something with low importance