About FFT of Exponential decay - two-sided
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Dear Forum
I just do the FFT of a Exponential decay - two-sided
Fs=512;
N=2.^12;
t=[-N/Fs/2:1/Fs:N/Fs/2-1/Fs];
S=exp(-2*abs(t));
The FFT is:
Y = fft(S,N);
Ayy = (abs(Y));
Ayy(1)=Ayy(1)/N;% to get the amplitude of zero frequency component
Ayy(2:end)=Ayy(2:end)/(N/2); %to get the amplitude of other frequencies
Ayy=fftshift(Ayy);
F=([-N/2:N/2-1])*Fs/N;
plot(F,Ayy);
My question is the FFT of the Exponential decay - two-sided is not 4/(4+F.^2)(F is the frequency vector) shown as follows:
F=([-N/2:N/2-1])*Fs/N;
Ground_Truth=4./(4+F.^2);
figure;
plot(Ground_Truth);
The Equations of the Exponential decay-two-sided and its corresponding Fourier transform can be found in the website of "Fourier transform of typical signals" as follows: http://fourier.eng.hmc.edu/e101/lectures/handout3/node3.html
Would you please tell me why "Ayy" is different from "Ground_Truth" according to my Matlab code?
Many Thanks Erick
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Miriam
il 8 Nov 2018
Hi Erick,
I think the problem lies in your definition of "Ground_Truth". Based on the website you linked to, it should be defined using angular frequency:
Ground_Truth=4./(4+(2*pi*F).^2);
2 Commenti
Miriam
il 9 Nov 2018
Hi Erick,
I would suggest normalizing Ayy as follows (after taking the absolute value):
Ayy = Ayy/max(Ayy);
and removing the other two lines modifying amplitude.
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