Why ifft results of analytic signal spectrum don't match with theoretical time formula?

Question

Jiali 2022-9-22

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1809920-why-ifft-results-of-analytic-signal-spectrum-don-t-match-with-theoretical-time-formula

评论： Jiali 2022-9-24

Dear all,

I need to convert a spectrum data back to time domain. Before it, I use a simple Gaussian pulse as a test. However, I found that results computed by ifft don't match with theoretical time equation. Why it happened? How to resolve it?

Fs=200;

T=1/Fs;

L=1200;

tau=0.4;

t0=2.8;

mag=10;

t=(0:L-1)*T;

f=Fs*(-L/2:L/2-1)/L;

Xf=@(x)sqrt(pi).*mag.*tau.*exp(-(2.*pi.*tau.*x).^2).*exp(-1i.*2.*pi.*x.*t0);

figure;

plot(f,real(Xf(f)));

% shift spectrum starting from 0 frequency

signal_comp=ifft(fftshift(Xf(f)).*L);

signal_theoretical=mag.*exp(-(t-t0).^2/tau^2);

figure;

plot(t,signal_theoretical);

hold on;

plot(t,real(signal_comp),'r--');

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Matt J 2022-9-22

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1809920-why-ifft-results-of-analytic-signal-spectrum-don-t-match-with-theoretical-time-formula#answer_1058565

编辑：Matt J 2022-9-22

在 MATLAB Online 中打开

The IFFT and the continuous inverse Fourier transform are not the same thing.

tau=0.4;

t0=2.8;

mag=10;

Fs=200;

dT=1/Fs;

L=2000;

dF=1/dT/L;

f=dF*(-L/2:L/2-1);

t=dT*(-L/2:L/2-1);

Xf=@(x)sqrt(pi).*mag.*tau.*exp(-(2.*pi.*tau.*x).^2).*exp(-1i.*2.*pi.*x.*t0);

% shift spectrum starting from 0 frequency

signal_comp= fftshift(ifft(ifftshift(Xf(f))) ) /dT; %note factor of 1/dT

signal_theoretical=mag.*exp(-((t-t0)/2).^2/tau^2)/2; %fix the theoretical formula

figure;

plot(t(1:20:end),signal_theoretical(1:20:end),'o',...

t,real(signal_comp),'r--');

legend('Theoretical','Computed',location='northwest')

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Jiali 2022-9-24

Thank you for your clarification! I do have misunderstanding between discrete Fourier transform and continuous Fourier transform although the concepts were taught before.

请先登录，再进行评论。