MATLAB: Why 50hz can’t be removed compeletely

50hz

Dear, I am try to remove the 50 hz. It works very well if I plot the result using amplitude. However when when I plot the result using 10*log10(amp), the 50hz will be still there with large amplitude.

%% build filter
N     = 20;    % Order
F3dB1 = 49;  % First
F3dB2 = 51;  % Second
Fs    = 1000;  % Sampling Frequency
d = designfilt('bandstopiir','FilterOrder',2, ...
               'HalfPowerFrequency1',49,'HalfPowerFrequency2',51, ...
               'DesignMethod','butter','SampleRate',Fs);
%% test data
fs = 1000;
t = 0:1/fs:5-1/fs;
x = cos(2*pi*50*t)+cos(2*pi*100*t);
%plot(t,x)
%plotChannelSpectral(x);
[psd,f] = pwelch(x,500,200,500,1000);
plot(f,10*log10(psd));
plot(f,(psd));
fdata=filtfilt(d,double(x));
[psd2,f2] = pwelch(fdata,500,200,500,1000);
figure;
plot(f2,psd2); % 50hz almost gone in this plot
plot(f,10*log10(psd2)); % however I still can see large 50hz in this plot, even I re-run the filtfilt 20 times, I still can see relative large amplitude around 50hz, though there is a groove at 50hz.

Does it means that I should be satisfied as long as I can't see the 50hz in amplitude? And there is no way to totally eliminate the large value under 10*log10(amplitude)?

Thanks in advance.

Best Answer

hello again

I like simple solutions - see demo code below adapted to your case

I hope 200 dB attenuation can be considered as "complete washed out" !!

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% 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');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')

Related Solutions

MATLAB: How to only pass the signals that I want

hello

this code will do fft / spectrogram and bandpass filtering - adapt the corner frequencies to your own needs !

clc
clear all
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 4096;    % 
OVERLAP = 0.5;
% spectrogram dB scale
spectrogram_dB_scale = 80;  % dB range scale (means , the lowest displayed level is XX dB below the max level)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% options 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% if you are dealing with acoustics, you may wish to have A weighted
% spectrums 
% option_w = 0 : linear spectrum (no weighting dB (L) )
% option_w = 1 : A weighted spectrum (dB (A) )
option_w = 1;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% data
% [data,Fs] = audioread('myWAVaudiofile.wav');
[data,Fs] = audioread('Immigran_Hiss.wav');
channel = 1;
signal = data(:,channel);
samples = length(signal);
%% decimate (if needed)
% NB : decim = 1 will do nothing (output = input)
decim = 1;
if decim>1
    signal = decimate(signal,decim);
    Fs = Fs/decim;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% display 1 : averaged FFT spectrum
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[freq, sensor_spectrum] = myfft_peak(signal,Fs,NFFT,OVERLAP);
% convert to dB scale (ref = 1)
sensor_spectrum_dB = 20*log10(sensor_spectrum);
% apply A weigthing if needed


if option_w == 1
    pondA_dB = pondA_function(freq);
    sensor_spectrum_dB = sensor_spectrum_dB+pondA_dB;
    my_ylabel = ('Amplitude (dB (A))');
else
    my_ylabel = ('Amplitude (dB (L))');
end
figure(1),plot(freq,sensor_spectrum_dB,'b');grid
title(['Averaged FFT Spectrum  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(freq(2)-freq(1)) ' Hz ']);
xlabel('Frequency (Hz)');ylabel(my_ylabel);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% display 2 : time / frequency analysis : spectrogram demo
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[sg,fsg,tsg] = specgram(signal,NFFT,Fs,hanning(NFFT),floor(NFFT*OVERLAP));  
% FFT normalisation and conversion amplitude from linear to dB (peak)

sg_dBpeak = 20*log10(abs(sg))+20*log10(2/length(fsg));     % NB : X=fft(x.*hanning(N))*4/N; % hanning only

% apply A weigthing if needed
if option_w == 1
    pondA_dB = pondA_function(fsg);
    sg_dBpeak = sg_dBpeak+(pondA_dB*ones(1,size(sg_dBpeak,2)));
    my_title = ('Spectrogram (dB (A))');
else
    my_title = ('Spectrogram (dB (L))');
end
% saturation of the dB range : 

% saturation_dB = 60;  % dB range scale (means , the lowest displayed level is XX dB below the max level)

min_disp_dB = round(max(max(sg_dBpeak))) - spectrogram_dB_scale;
sg_dBpeak(sg_dBpeak<min_disp_dB) = min_disp_dB;
% plots spectrogram

figure(2);
imagesc(tsg,fsg,sg_dBpeak);colormap('jet');
axis('xy');colorbar('vert');grid
title([my_title ' / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(fsg(2)-fsg(1)) ' Hz ']);
xlabel('Time (s)');ylabel('Frequency (Hz)');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% removal of hiss between t = 0 and t = 1.68 s
% use of bandpass filter to remove noise below 500 and above 2500 Hz
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
data_filtered = data;
t_min = 0;
t_max = 1.68;
ind = 1+fix(t_min*Fs:t_max*Fs-1);
% keep only signal content extracted by bandpass filters 
f_low = 500;
f_high = 2500;
N = 4;
% signal_filtered = zeros(size(signal));
[b,a] = butter(N,2/Fs*[f_low f_high]);
% now let's filter the signal
data_filtered(ind,:) = filtfilt(b,a,data(ind,:));
% save as wav file 
audiowrite('Immigran_Hiss-filt.wav',data_filtered,Fs);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 2B : time / frequency analysis : spectrogram demo
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[sg,fsg,tsg] = specgram(data_filtered(:,1),NFFT,Fs,hanning(NFFT),floor(NFFT*OVERLAP));  
% FFT normalisation and conversion amplitude from linear to dB (peak)
sg_dBpeak = 20*log10(abs(sg))+20*log10(2/length(fsg));     % NB : X=fft(x.*hanning(N))*4/N; % hanning only
% apply A weigthing if needed
if option_w == 1
    pondA_dB = pondA_function(fsg);
    sg_dBpeak = sg_dBpeak+(pondA_dB*ones(1,size(sg_dBpeak,2)));
    my_title = ('Spectrogram (dB (A))');
else
    my_title = ('Spectrogram (dB (L))');
end
% saturation of the dB range : 
% saturation_dB = 60;  % dB range scale (means , the lowest displayed level is XX dB below the max level)
min_disp_dB = round(max(max(sg_dBpeak))) - spectrogram_dB_scale;
sg_dBpeak(sg_dBpeak<min_disp_dB) = min_disp_dB;
% plots spectrogram
figure(3);
imagesc(tsg,fsg,sg_dBpeak);colormap('jet');
axis('xy');colorbar('vert');grid
title([my_title ' / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(fsg(2)-fsg(1)) ' Hz ']);
xlabel('Time (s)');ylabel('Frequency (Hz)');
function pondA_dB = pondA_function(f)
	% dB (A) weighting curve
	n = ((12200^2*f.^4)./((f.^2+20.6^2).*(f.^2+12200^2).*sqrt(f.^2+107.7^2).*sqrt(f.^2+737.9^2)));
	r = ((12200^2*1000.^4)./((1000.^2+20.6^2).*(1000.^2+12200^2).*sqrt(1000.^2+107.7^2).*sqrt(1000.^2+737.9^2))) * ones(size(f));
	pondA = n./r;
	pondA_dB = 20*log10(pondA(:));
end
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 overlap % (between 0 and 0.95)
samples = length(signal);
% fill signal with zeros if its length is lower than nfft
if samples<nfft
    s_tmp = zeros(nfft,1);
    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;
        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

MATLAB: 50 Hz interference and noise reduction from ECG.

hello

If you want only to remove the 50 Hz tone , use a notch filter as shown in example below. I used your data and guessed the sampling frequency from the fact that the peak was at 50 Hz.

So sampling at 10 kHz is pretty high for an ECG signal, you could easily go down by factor 10.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% data
signal = importdata('Sinal1.txt');
dt = 1e-4; % 0.1 milli seconds
samples = length(signal);
Fs = 1/dt; % sampling frequency (Hz)
%% decimate (if needed)
% NB : decim = 1 will do nothing (output = input)
decim = 1;
if decim>1
    signal = decimate(signal,decim);
    Fs = Fs/decim;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = Fs;    % 
Overlap = 0.75;
w = hanning(NFFT);     % Hanning window / Use the HANN function to get a Hanning window which has the first and last zero-weighted samples.
%% notch filter section %%%%%%
% H(s) = (s^2 + 1) / (s^2 + s/Q + 1)
fc = 50;       % notch freq
wc = 2*pi*fc;
Q = 7;         % 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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[freq,fft_spectrum] = myfft_peak(signal, Fs, NFFT, Overlap);
sensor_spectrum_dB = 20*log10(fft_spectrum);% convert to dB scale (ref = 1)

[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),semilogx(freq,sensor_spectrum_dB,'b',freq,sensor_spectrum_filtered_dB,'r');grid on
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')
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 overlap % (between 0 and 0.95)
signal = signal(:);
samples = length(signal);
% fill signal with zeros if its length is lower than nfft
if samples<nfft
    s_tmp = zeros(nfft,1);
    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;
        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

Best Answer

Related Solutions

MATLAB: How to only pass the signals that I want

MATLAB: 50 Hz interference and noise reduction from ECG.

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