You cannot reliably invert a Fourier transforom unless you also have the phase information. Lacking the phase information, you can still invert it, however the result will not be reliable and may not reflect the actual time-domain signal. The best approach is to record the time-domain signal and calculate the Fourier transform afterwards.
One approach —
RL = readlines('550mvp.csv');
H1 = split(RL(1,:),',');
H2 = split(RL(2,:),',');
T1 = readtable('550mvp.csv', 'HeaderLines',2);
T1.Properties.VariableNames = H1.'
NrMissing = nnz(ismissing(T1))
T1 = fillmissing(T1, 'linear');
figure
plot(T1{:,1}, T1{:,2})
grid
xlabel(H2(1,:))
ylabel(H2(2,:))
L = height(T1)
Fn = max(T1{:,1}); % Nyquist Frequency
Fs = Fn*2; % Sampling Frequency
Ts = 1/Fs; % Sampling Interval
Lt = 2*L; % Assumed Length Of Original Time-Domain Signal
t = linspace(0, Lt-1, Lt)/Fs; % Time Vector
v = ifft([T1{:,2}; flip(T1{:,2})],'symmetric');
figure
plot(t, v)
grid
xlabel('Time')
ylabel('Volt')
xlim([min(t) max(t)])
figure
plot(t, v)
grid
xlabel('Time')
ylabel('Volt')
xlim([min(t) 1E-6])
This initially re-creates the full ‘original’ two-sided Fourier ttransform by appending a flipped version of the original one-sided Fourier transform to it and then doing the inversion. The highest frequency is assumed to be the Nyquist frequency here, and the sampling frequency and sampling intervals are calculatted from it.
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EDIT — Corrected typographical errors.
EDIT — (14 Jul 2024 at 13:24)
Forgot the symmetry flag in the ifft call. Added now.
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