How to make Narrow Bandpass filter?

I have a signal, that has a bunch of noise and sine signals in it, 4 sine signals too be exact, and 4 noise signals.

i have pin pointed the frequencies of these sine signals to be 159.0574, 359.3519, 459.4992, 709.8674.

The signal and its spektrum looks like this:

I need to filter out all the noise, so i tried too use bandpass, using each sine frequency :

f1 = bandpass(signalas, [floor(virsunes(1)) ceil(virsunes(1))], Fd);

f2 = bandpass(signalas, [floor(virsunes(2)) ceil(virsunes(2))], Fd);

f3 = bandpass(signalas, [floor(virsunes(3)) ceil(virsunes(3))], Fd);

f4 = bandpass(signalas, [floor(virsunes(4)) ceil(virsunes(4))], Fd);

virsunes is just an array of those frequencies.

When i combined the filtered signals, i got this:

A lot of the noise has stuck around because it's too close too the sine signal. How to make a bandpass filter more narrow, for it too filter all the noise?

I attached the signal file "G4_12.dot".

Answer 1

[Mathieu NOE]

hello

seems I have already seen similar post somewhere... a buddy of yours ?

you did not mentionned the sampling frequency , but 24 kHz seemed correct

here my little contribution :

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% options 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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


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

%% test data
Fs = 24000;
% t = 0:1/Fs:10-1/Fs;
fid = fopen('G4_12.dat','r')
[signal,samples] = fscanf(fid, '%12f');
fclose(fid);

% decimate
decim = 12;
signal = decimate(signal,decim);
Fs = Fs/decim;
samples = length(signal);
time =(1:samples)/Fs;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
n_max = fix(log2(samples));
NFFT = 2^(n_max-1);    % 2^n with n chosen so that NFFT is below length of signal (even after decimation) by factor > 2 so some averaging is doable
% NFFT = 2048/4;    % 2^n with n chosen so that NFFT is below length of signal (even after decimation) by factor > 2 so some averaging is doable
NOVERLAP = round(0.95*NFFT);
w = hanning(NFFT);     % Hanning window / Use the HANN function to get a Hanning window which has the first and last zero-weighted samples.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display : averaged FFT spectrum before filter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[sensor_spectrum, freq] = pwelch(signal,w,NOVERLAP,NFFT,Fs,'power');
sensor_spectrum_dB = 10*log10(sensor_spectrum);% convert to dB scale (ref = 1)
% sensor_spectrum_dB = sensor_spectrum_dB-min(sensor_spectrum_dB); % y axis shift so dB values are positive (min value = 0)

%% findpeaks
% df = Fs/NFFT;
% MAXW = 10*df;
% MPD = 20;
% MPP = 20;
% [peaks,loc,W,P] = findpeaks(sensor_spectrum_dB,'MinPeakDistance',MPD,'MaxPeakWidth',MAXW,'MinPeakProminence',MPP);
% freq_peaks = freq(loc);
freq_peaks = [159.0574, 359.3519, 459.4992, 709.8674];
peaks = interp1(freq,sensor_spectrum_dB,freq_peaks,'linear');
figure(1),plot(freq,sensor_spectrum_dB,'b',freq_peaks,peaks,'*r');grid
title(['Averaged FFT Spectrum  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(freq(2)-freq(1)) ' Hz ']);
xlabel('Frequency (Hz)');ylabel(' dB')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 2 : time / frequency analysis : spectrogram demo
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[sg,fsg,tsg] = specgram(signal,NFFT,Fs,hanning(NFFT),NOVERLAP);  

% 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

% scalingf the dB range : 
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(['Spectrogram / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(fsg(2)-fsg(1)) ' Hz ']);
xlabel('Time (s)');ylabel('Frequency (Hz)');

% keep only signal content extracted by bandpass filters 
fc = freq_peaks;      % Hz
bandwith = 8;      % Hz
f_low = fc-0.5*bandwith;
f_high = fc+0.5*bandwith;
N = 4;
signal_filtered = zeros(size(signal));

for ci = 1:length(fc)
    [b,a] = butter(N,2/Fs*[f_low(ci) f_high(ci)]);
    % add filtered signal to total final signal
    tmp = filtfilt(b,a,signal);
    signal_filtered = signal_filtered + tmp;
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display : averaged FFT spectrum before / after notch filter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[sensor_spectrum_filtered, freq] = pwelch(signal_filtered,w,NOVERLAP,NFFT,Fs,'power');
sensor_spectrum_filtered_dB = 10*log10(sensor_spectrum_filtered);% convert to dB scale (ref = 1)

figure(4),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 filter','after filter');
xlabel('Frequency (Hz)');ylabel(' dB')

figure(5),plot(time,signal_filtered,'b');grid
title('Filtered signal');
xlabel('Time (s)');ylabel(' amplitude')

[mathew mathew]

Ah, similar you say? It might have been one of my colleagues.

And yes, it is 24 kHz. So that may confirm it.

Wow, you even made a spectogram.

If it was my colleague, you might have guessed why i needed the noise filtered.

In addition to finding the sine signal frequencies, i have too find the bigining time of the sine signals, and end times.

The spectogram i made previously looked like this, after bandpass filter:

it looks pretty bad. the quality of the spektrogram is poor, and i was afraid i wouldn't be able too get accurate results, because of that, espesialy with the sine signal that is realy close too the noise signal. So that was the reason i wanted all the noise filtered.

I added a spektogram simiular too yours with the filtered signal, just too see how it looks.

But it seems, with your spektrogram, filtering might not even be necessary too finde the bigining time and end times of the sine signals.

[Mathieu NOE]

With STFT (short time fourier transform) , which is the basement of spectrogram, it may be difficult to obtain a good compromise between frequency resolution and time resolution.

i found in this specific case that to separate the sinus from the noise bands we needed a refined frequency resolution (df< 2 Hz) , but that does not give a very attractive time resolution

so my suggestion (to your colleague) was to look at each of the bandpass filtered signal, to rectify it, to make an enveloppe of that and to detect when that enveloppe goes above a certain (positive) threshold :

• when it crosses the enveloppe with a positive slope it's the beginning of the signal
• when it crosses the enveloppe with a negative slope it's the end of the signal

IMHO, it's much better than to rely on readings from the spectrogram