Using IFFT to get original signal and Parseval's Theorem

问题

I have a current signal (extracted in csv) which I obtained from cadence simulation over 30ns time. I have removed DC offset and applied windowing function before FFT. And normalized FFT by sqrt(N). I have shift zero-frequency component to center of my desired spectrum with fftshift(X). I got my desired FFT. I also want to get back to my original windowed signal by ifft but it is not showing my windowed signal instead it is showing only a version of the window function that I used. My sample signal is real not complex.

I have another question. My power before FFT and after FFT is same. How can I show in graph in an intelligent way to show Parseval's theroem?

I have also added my MATLAB code without the uploading csv and making the vectors. my y value is Current_wo_dc

MATLAB Code:

N = length(Current_wo_dc);
ts = 1.0e-12;
Fs = 1/ts;
tmax = (N-1)*ts;
tm = 0:ts:tmax;
f = -Fs/2:Fs/(N-1):Fs/2;

fn=hanning(N);  % hanning window function
Z = Current_wo_dc'.*fn; 

Power_Z = sum(Z.^2); % power in time domain

%FFT
fftY = fft(Z);
y = fftshift(fftY);
Y = abs(y);
a3 = Y/sqrt(N);

Power_fftY = sum(fftY.*conj(fftY))/length(fftY); % power in frequency domain

%IFFT:
I = ifftshift(fftshift(Z));
II = I*sqrt(N);

%PSD
psd = a3.^2;
psd_db = 10*log10(psd);

subplot(311), plot(Z); % windowed signal
subplot(312), plot(a3); % fft across frequency bin not shifted along frequency
subplot(313), plot(II); % ifft 

来源：https://stackoverflow.com/questions/44776612/using-ifft-to-get-original-signal-and-parsevals-theorem