How to use bandpass filter.

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Dung Nguyen 2019-6-24

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评论： Dung Nguyen 2021-7-13

I have a data set which includes 2 columns: one is time (in month) and one is values that need analysics. I need to used bandpass filer to filter signal and obtain quasi-beninial oscillation (QBO) as figure 6(in attach). The period of this QBO is from 22 to 34 months, centered at 28 months. I try wirte a code but I don't belive on it. I would like everyone to check help me. My data, code, figure in attach. I hope everyone can help me.

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Answer 1

Mathieu NOE 2021-7-8

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Hello

no bugs or special issues , but minor improvements

I prefer to use the IIR filters (like butter) used with filtfilt

clc;clear all;close all
load RTEC_N1.txt
time=RTEC_N1(:,1);
RTEC=RTEC_N1(:,2);
%% dt 
dt = mean(diff(time));
% fnorm_12=[1./28 1./24];
Fs=1/dt;
fc1 = 1./30;
fc2=1./22;
Wn = (2/Fs)*[fc1 fc2];
% Wn = [(2/Fs)*fc1 (2/Fs)*fc2];
% b = fir1(10,Wn,'low',kaiser(11,3));
% wn=[1./30 1./22];
% [b,a] = fir1(75,Wn);
% [b,a] = fir1(80,Wn,'bandpass');
% wn=1./(fs/2)/26
[b,a]=butter(2,Wn);
yy = filtfilt(b,a,RTEC);
% yy = filter(b,a,RTEC);
% figure(1);
% plot(time,RTEC,time,y,time,yy)
% legend('Original','filtfilt','filter');grid on;
plot(time,RTEC,'b',time,yy,'r');grid on;hold on;
fid1=fopen('RTIME_Sfiltertry1.txt','w');
for i=1:length(time)
    fprintf(fid1,'%10.3f\t%10.4f\r\n',time(i),yy(i));
end
fclose(fid1);

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Mathieu NOE 2021-7-9

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hello

so when I am in doubt I do a fft analysis first to see where the signals has strong peaks in the spectrum .. here we have multiple peaks , and maybe the one around period = 26 months is the one you are looking for; then you can define the best filter parameters ...

updated code below :

clc;clear all;close all
load RTEC_N1.txt
time=RTEC_N1(:,1);  % time (in month)
RTEC=RTEC_N1(:,2);
%% dt 
dt = mean(diff(time));
Fs=1/dt;  % unit : 1 / month
%% first FFT analysis
    NFFT = length(RTEC);    % so freq resolution is highest
    OVERLAP = 0;
    [freq, sensor_spectrum] = myfft_peak(RTEC,Fs,NFFT,OVERLAP);
    % remove data for freq < 1/40 month and freq > 1/10 month ;
    ind=find(freq>1/40 & freq<1/10);
    freq = freq(ind);
    sensor_spectrum = sensor_spectrum(ind);
    %%%%
    period = 1./freq ; % period in month
    figure(1),plot(period,sensor_spectrum,'b');
    title('FFT Spectrum');
    xlabel('Frequency ( 1 / month)');ylabel('Amplitude');
    xlabel('Period ( month)');ylabel('Amplitude');
%%% then filtering
fc = 1/26;  % estimated central frequency 
fc1 = fc/1.2; % lower  and higher cut off filter frequencies are symetrical from fc with a factor of 1.2
fc2 = fc*1.2;
Wn = (2/Fs)*[fc1 fc2];
[b,a]=butter(2,Wn);
yy = filtfilt(b,a,RTEC);
figure(2),plot(time,RTEC,'b',time,yy,'r');grid on;hold on;
% write results
writematrix([time(:) yy(:)], 'RTIME_Sfiltertry1.txt',"Delimiter","tab");
%% second FFT analysis
    NFFT = length(RTEC);    % so freq resolution is highest
    OVERLAP = 0;
    [freq, sensor_spectrum1] = myfft_peak(RTEC,Fs,NFFT,OVERLAP);
    [freq, sensor_spectrum2] = myfft_peak(yy,Fs,NFFT,OVERLAP);
    %%%%
    period = 1./freq ; % period in month
    figure(3),semilogx(period,sensor_spectrum1,'b',period,sensor_spectrum2,'r');
    title('FFT Spectrum');
    xlabel('Frequency ( 1 / month)');ylabel('Amplitude');
    legen('raw data','filtered data');
    xlabel('Period ( month)');ylabel('Amplitude');
    
    
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

Mathieu NOE 2021-7-13

hello

well, your eyes are more powerful than any spectral analysis tool !! some tools are more appropriate than others for non stationnary signals (like wavelet vs fft) , but as already said above, there is some trace of the 26-28 month period signal but it's weak; does it means there is a problem with the data ? honestly , i cannot say because my field of expertise is more industrial vibration analysis and control , rather than weather or oceanographic data .

I may come to the point where my help is coming to and end - sorry for that

Dung Nguyen 2021-7-13

Hello

Thanks for your help.

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How to use bandpass filter.

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