I have no idea what you want. I would not suggest integrating the individual sine and cosone coefficients using numerical integration. The Fast Fourier Transform calculates the coefficients much more efficiently.
T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/987480/data.txt');
T1.Properties.VariableNames = {'Signal','Time'}
figure
plot(T1.Time, T1.Signal)
grid
xlabel('Time')
ylabel('Amplitude')
L = size(T1,1);
Ts = mean(diff(T1.Time)); % Sampling Interval
Fs = 1/Ts; % Sampling Frequency
Fn = Fs/2; % Nyquist Frequency
FTSignal = fft(T1.Signal-mean(T1.Signal))/L; % Fourier Transform (Subtract Mean To Emphasize Peaks)
Fv = linspace(0, 1, fix(L/2)+1)*Fn; % Frequency Vector
Iv = 1:numel(Fv); % Index Vector
figure
plot(Fv, abs(FTSignal(Iv))*2)
grid
xlabel('Frequency')
ylabel('Amplitude')
xlim([0 5]*1E+7)
The coefficients of the cosine (real) terms are the real parts of ‘FTSignal’ and the imaginary parts are the coefficients of the sine terms for each frequency in the ‘Fv’ vector.
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