Automatic Signal denoising and segmenting for feature extraction

Can you help me to denoise this signal using 4th order bandpass butterwoth filter and make a segment for 8 sec of data and shifted by 2 sec of data for the whole data length.

[Amir Hamzah]

fs = 125Hz

Answer 1

[Mathieu NOE]

hello

this is a code to implement a 4th order bandpass filter (and plot the fft spectrum of the signal before and after filtering)

NB : the filter order in the code is 2 but applied twice with filtfilt , so the outpt signal has zero phase lag but is actually filtered twice.

I cannot decide by myself what are the frequency range to focus (so low and high cut off frequencies for the filter must be adapted)

also I cannot decide which 8 seconds portion of the signal among the + 300 s of raw data is of interest for you

this also is unclear to me : shifted by 2 sec

code :

clc
clearvars

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

filename = ('matlab.mat'); 
data = load(filename);
signal = (data.unnamed)';
Fs = 125; % sampling rate is 125 Hz
dt = 1/Fs;

[samples,channels] = size(signal);

% time vector 
time = (0:samples-1)*dt;

% keep 8 seconds of data 
t_start = 1; % second
duration = 8; % second
ind = (time>=t_start & time<=t_start+duration);
time = time(ind);
signal = signal(ind);


%% band pass  filter section %%%%%%
    f_low = 1;
    f_high = 10;
    N_bpf = 2;           % filter order
    [b,a] = butter(N_bpf,2/Fs*[f_low f_high]);
    signal_filtered = filtfilt(b,a,signal);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 1000;    % 
OVERLAP = 0.75;


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 1 : time domain plot
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(1),
subplot(211),plot(time,signal,'b');grid on
title(['Time plot  / Fs = ' num2str(Fs) ' Hz / raw data ']);
xlabel('Time (s)');ylabel('Amplitude');
subplot(212),plot(time,signal_filtered,'r');grid on
title(['Time plot  / Fs = ' num2str(Fs) ' Hz / filtered data ']);
xlabel('Time (s)');ylabel('Amplitude');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 2 : averaged FFT spectrum
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[freq, spectrum_raw] = myfft_peak(signal,Fs,NFFT,OVERLAP);
[freq, spectrum_filtered] = myfft_peak(signal_filtered,Fs,NFFT,OVERLAP);

figure(2),plot(freq,20*log10(spectrum_raw),'b',freq,20*log10(spectrum_filtered),'r');grid on
df = freq(2)-freq(1); % frequency resolution 
title(['Averaged FFT Spectrum  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(df,3) ' Hz ']);
xlabel('Frequency (Hz)');ylabel('Amplitude (dB)');
legend('raw','filtered');

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