using acceleration record, Get velocity and displacement signal & carry out FFT and plot the spectra

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Given information
  • Time domain signal file : GEE Earthquke.xlsx (attached)
  • Sampling rate (frequency): 64Hz
  • Acceleration values in g (9.81m/s^2)
1) Velocity and displacement signal
  • Consider baseline correction
  • Get the relative velocity and displacement signals
  • Plot the signals
  • Get the amplitude parameters in time domain (peak acceleration, peak velocity and peak displacement)
2) Carry out the FFT and plot the spectra
P.S No matter how much I think and try, I can't code.. plz help me

Accepted Answer

Mathieu NOE
Mathieu NOE on 30 Mar 2022
hello
see my suggestion below
clc
clearvars
data = readmatrix('GEE Earthquake.xlsx');
t = data(:,1);
dt = mean(diff(t)); % Average dt
fs = 1/dt; % Frequency [Hz] or sampling rate
% Acceleration data
acc = data(:,2)*9.81; % Add gravity factor ( g to m/s²)
acc = detrend(acc); % baseline correction
% some additionnal high pass filtering % baseline correction
N = 2;
fc = 0.25; % Hz
[B,A] = butter(N,2*fc/fs,'high');
acc = filter(B,A,acc);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
velocity = cumtrapz(dt,acc);
velocity = detrend(velocity); % baseline correction
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp = cumtrapz(dt,velocity);
disp = detrend(disp); % baseline correction
%
figure(1)
subplot(311),plot(t,acc);
title('accel'); ylabel('m/s²');xlabel('time (s)');
subplot(312),plot(t,velocity);
title('velocity'); ylabel('m/s');xlabel('time (s)');
subplot(313),plot(t,disp);
title('disp'); ylabel('m');xlabel('time (s)');
%%fft
nfft = length(acc);
fft_spectrum = (abs(fft(disp,nfft))/nfft);
% 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;
figure(2)
plot(freq_vector,fft_spectrum);
title('disp'); ylabel('m');xlabel('time (s)');
xlim([0 10]);
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