implements a digital notch filter to remove the frequency component at 1 Hz.

I have a file named X that has data points sampled at 400Hz , time between samples (0.0025sec)

I have been asked to implements a digital notch filter to remove the frequency component at 1 Hz.

using the difference equation:

y(n)=G*[X(n)-2*cos(w0)*X(n-1)+X(n-2)]+[2*p cos(w0)*y(n-1)-p^2 y(n-2)]

where : X(n) my data file X, G=1, p=0.99, w0= 0.0157, n= length(X-1).

I have all the information to implement the equation, but when I use it, it tells me Unrecognized function or variable 'y'.

[Mathieu NOE]

hello

can you share your code ?

[BoBo]

For file X I copied the data column and paset it into an array type double. 1x1930

Fs=400,

Fo=1,

T=0.0025,

G=1,

n= length(X-1)

p=0.99,

w0=0.0157,

y(n)=G*[X(n)-2*cos(w0)*X(n-1)+X(n-2)]+[2*p cos(w0)*y(n-1)-p^2 y(n-2)]

Answer 1

[Mathieu NOE]

hello

see example code below

clc
clearvars

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% dummy data
Fs = 400;
samples = 2000;
t = (0:samples-1)'*1/Fs;
signal = sin(2*pi*1*t)+0.02*sin(2*pi*50*t)+1e-2*randn(samples,1); % two sine + some noise



%% notch filter section %%%%%%
% y(n)=G*[x(n)-2*cos(w0)*x(n-1)+x(n-2)]+[2*p cos(w0)*y(n-1)-p^2 y(n-2)]
% this difference equation can be converted to IIR filter numerator /
% denominator
fc = 1;       % notch freq
w0 = 2*pi*fc/Fs;
p = 0.99;

% digital notch (IIR)
num1z=[1 -2*cos(w0) 1];
den1z=[1 -2*p*cos(w0) p^2];

% now let's filter the signal 
signal_filtered = filtfilt(num1z,den1z,signal);

figure(1),plot(t,signal,'b',t,signal_filtered,'r');grid
title('Signal');
legend('before notch filter','after notch filter');
xlabel('Time (s)');ylabel(' Amplitude')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display : averaged FFT spectrum before / after notch filter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 400;
Overlap = 0.75;

[freq,fft_spectrum] = myfft_peak(signal, Fs, NFFT, Overlap); %
sensor_spectrum_dB = 20*log10(fft_spectrum);% convert to dB scale (ref = 1)

% demo findpeaks
[pks,locs]= findpeaks(sensor_spectrum_dB,'SortStr','descend','NPeaks',2);

[freq,fft_spectrum_filtered] = myfft_peak(signal_filtered, Fs, NFFT, Overlap);
sensor_spectrum_filtered_dB = 20*log10(fft_spectrum_filtered);% convert to dB scale (ref = 1)

figure(2),plot(freq,sensor_spectrum_dB,'b',freq,sensor_spectrum_filtered_dB,'r');grid
title(['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')
text(freq(locs)+1,pks,num2str(freq(locs)))


function  [freq_vector,fft_spectrum] = myfft_peak(signal, Fs, nfft, Overlap)
% FFT peak spectrum of signal  (example sinus amplitude 1   = 0 dB after fft).
% Linear averaging
%   signal - input signal, 
%   Fs - Sampling frequency (Hz).
%   nfft - FFT window size
%   Overlap - buffer percentage of overlap % (between 0 and 0.95)

[samples,channels] = size(signal);

% fill signal with zeros if its length is lower than nfft
if samples<nfft
    s_tmp = zeros(nfft,channels);
    s_tmp((1:samples)) = signal;
    signal = s_tmp;
    samples = nfft;
end

% window : hanning
window = hanning(nfft);
window = window(:);

%    compute fft with overlap 
 offset = fix((1-Overlap)*nfft);
 spectnum = 1+ fix((samples-nfft)/offset); % Number of windows
%     % for info is equivalent to : 
%     noverlap = Overlap*nfft;
%     spectnum = fix((samples-noverlap)/(nfft-noverlap));	% Number of windows

    % main loop
    fft_spectrum = 0;
    for i=1:spectnum
        start = (i-1)*offset;
        sw = signal((1+start):(start+nfft),:).*(window*ones(1,channels));
        fft_spectrum = fft_spectrum + (abs(fft(sw))*4/nfft);     % X=fft(x.*hanning(N))*4/N; % hanning only 
    end
    fft_spectrum = fft_spectrum/spectnum; % to do linear averaging scaling

% one sidded fft spectrum  % Select first half 
    if rem(nfft,2)    % nfft odd
        select = (1:(nfft+1)/2)';
    else
        select = (1:nfft/2+1)';
    end
fft_spectrum = fft_spectrum(select,:);
freq_vector = (select - 1)*Fs/nfft;
end