digital filter designdigital signal processingsimulink
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%NFFT = 1024*4; %
NOVERLAP = round(0.75*NFFT);w = hanning(NFFT); % Hanning window / Use the HANN function to get a Hanning window which has the first and last zero-weighted samples.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% test data
Fs = 1000;t = 0:1/Fs:10-1/Fs;signal = cos(2*pi*50*t)+cos(2*pi*100*t); %% notch filter section %%%%%%
% H(s) = (s^2 + 1) / (s^2 + s/Q + 1)
fc = 50; % notch freq
wc = 2*pi*fc;Q = 2; % adjust Q factor for wider (low Q) / narrower (high Q) notch
% at f = fc the filter has gain = 0
w0 = 2*pi*fc/Fs;alpha = sin(w0)/(2*Q); b0 = 1; b1 = -2*cos(w0); b2 = 1; a0 = 1 + alpha; a1 = -2*cos(w0); a2 = 1 - alpha; % analog notch (for info)
num1=[1/wc^2 0 1];den1=[1/wc^2 1/(wc*Q) 1];% digital notch (for info)
num1z=[b0 b1 b2];den1z=[a0 a1 a2];freq = linspace(fc-1,fc+1,200);[g1,p1] = bode(num1,den1,2*pi*freq);g1db = 20*log10(g1);[gd1,pd1] = dbode(num1z,den1z,1/Fs,2*pi*freq);gd1db = 20*log10(gd1);figure(1);plot(freq,g1db,'b',freq,gd1db,'+r');title(' Notch: H(s) = (s^2 + 1) / (s^2 + s/Q + 1)');legend('analog','digital');xlabel('Fréquence (Hz)');ylabel(' dB') % now let's filter the signal
signal_filtered = filtfilt(num1z,den1z,signal);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display : averaged FFT spectrum before / after notch filter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%[sensor_spectrum, freq] = pwelch(signal,w,NOVERLAP,NFFT,Fs);sensor_spectrum_dB = 20*log10(sensor_spectrum);% convert to dB scale (ref = 1)
[sensor_spectrum_filtered, freq] = pwelch(signal_filtered,w,NOVERLAP,NFFT,Fs);sensor_spectrum_filtered_dB = 20*log10(sensor_spectrum_filtered);% convert to dB scale (ref = 1)figure(2),semilogx(freq,sensor_spectrum_dB,'b',freq,sensor_spectrum_filtered_dB,'r');gridtitle(['Averaged FFT Spectrum / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(freq(2)-freq(1)) ' Hz ']);legend('before notch filter','after notch filter');xlabel('Frequency (Hz)');ylabel(' dB')
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