Automatic Signal denoising and segmenting for feature extraction

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Amir Hamzah
Amir Hamzah on 11 Apr 2022
Answered: Mathieu NOE on 11 Apr 2022
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.

Accepted Answer

Mathieu NOE
Mathieu NOE on 11 Apr 2022
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

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