adaptive lms notch filter is IIR or FIR?

Started by March 14, 2008
hi im doing a project regarding development of an adptive digital notch filter for the removal of 50hz noise from an ecg signal.i have the my problem is when do the full report for methodology.first I explained about adaptive filter and followed by adaptive notch filter..then I explained about LMS algorithm seems the sign regressor algorithm comes under LMS..the thing is im confused with this method like it comes under IIR or FIR..because there also LMS related with IIR and FIR..from what I studied adaptive notch filter always related to FIR and also IIR..LMS notch filter code comes under IIR or FIR?could anyone briefly explain to me?it will make to understand the flow of this code working better..thank you

clear all
load data
Fs = 500;
N = 900;
i = [0 : N-1]';

xa(1:N)+5*sin(2*pi*50* i/Fs)+10*sin(2*pi*48* i/Fs);
u = sin(2*pi*50* i/Fs);

%adaptive filter architecture
L = 20;
step_size = 0.005;
w = zeros(1,L);

%run the adaptive filter
e(L) = x(L);
for k = L : N
regressor = flipud(u(k-L+ 1:k));
w = w + step_size * regressor' * e(k);
e(k+1) = x(k) - w * regressor;

%compute the spectrum of the initial signal and the filtered signal
f = [0 : Fs/N : Fs/2 - Fs/N]';
F = abs(fft(x));
E = abs(fft(e));

subplot(411) ;plot(x); title('initial signal');
subplot(412) ;plot(e(2:N+1)); title('initial signal after filtering');
subplot(413) ;plot(f,F( 1:length( f)));title( 'spectrum of initial signal');
subplot(414) ;plot(f,E( 1:length( f)));title( 'spectrum of initial signal after filtering');

the key to understanding this code, is first understanding the various signals that appear in it. First of all x is the initial signal containing a component of 50Hz which you want to remove by adaptive filtering. This signal will play the role of the desired signal. Since we want to remove the frequency component of 50Hz, the reference signal u must be a sinusoid of 50Hz. Now, the LMS adaptive filter will try to use the reference signal u and from it predict/estimate the desired signal x. So, the output of the adaptive filter, namely u*w, will be as close as possible to the desired signal x. But since u contains only one frequency, then the output of the adaptive filter will be an estimation of the corresponding frequency component in the desired signal, if such one exists. Consequently u*w will be an accurate approximation of the 50Hz component in x. Now, the error signal of the adaptive filter is simply e=x-u*w, but based on the above analysis e will be the initial signal with the 50Hz component removed! Now this process is an IIR process. One way to think of that is that the input to the overall system is x and the output is e. Hence the transfer function E(z)/D(z) should indicate whether the filtering is IIR or FIR. If you find this transfer function ("Fundamentals of Adaptive Filtering",Ali Sayed, problem 5.14/page 261), then this is a transfer function of an IIR notch filter! The derivation of the transfer function is somehow elaborate but you can try it anyway.

Manolis C. Tsakiris
please refer the book " digital signal processing" using matlab by vinay k.kale and john g. proakis {BookWare Companian Series}
-- shankar