Thread Subject:

using ifft to get original signal back

I have two equations, one in the frequency domain (gf) and the other one in the time domain (gt). I used ifft to reconstruct the original function in the time domain (gt2). However, I couldn’t get back the original one. I was thinking there might a scaling issue. So, I applied followings: gt2.*N, gt2./N, gt2.*df, … none of them worked! this is my code:

% Time and frequency range
T=1000;
df=1/T;
N=60000;
f=eps:df:(N-1)*df; % Frequency range
t=T/2*linspace(eps,1,N);
w=2*pi.*f; % Angular frequency

%Function in the frequency domain
alph=(1+i).*sqrt(w/2);
gf=((1./(2*alph))).* exp(-alph.*2);
 
%Function in the time domain
gt = exp(-1./t)./(4*pi*t).^(1/2);
 
% Inverse Fourier transform
 gt2=ifft(gf,N);

 figure(1)
 plot(t,real(gt))
 figure(2)
 plot(t,real(gt2))

I also changed my time and frequency range to include both positives and negatives (to see if that make a change) as the following. (A small value of eps was also added to each t or f in the equations to avoid NaN in zero frequency and time). I also applied ifftshift and switched positive and negative time components
gt22= ifft(ifftshift(gf)), gt2 = [gt22((round(N/2)+1):end) gt22(1:round(N/2))];
but it gave me a weird shape!

%New time and frequency range
df = 0.01;
fmax=10;
f = -fmax:df:fmax;
dt=1/(2*fmax);tmax=round((1/df)/2);
t = -tmax:dt:tmax;
N = length(f);
 
I also saw a similar post on this problem but it didn't help me . I would appreciate your help and suggestion.

Thank you
sharmin

"sharmin shamsalsadati" <sharmin_shamsalsadati@yahoo.com> wrote in message <jmmudh$705$1@newscl01ah.mathworks.com>...
> I have two equations, one in the frequency domain (gf) and the other one in the time domain (gt). I used ifft to reconstruct the original function in the time domain (gt2). However, I couldn’t get back the original one. I was thinking there might a scaling issue. So, I applied followings: gt2.*N, gt2./N, gt2.*df, … none of them worked! this is my code:
>
> % Time and frequency range
> T=1000;
> df=1/T;
> N=60000;
> f=eps:df:(N-1)*df; % Frequency range
> t=T/2*linspace(eps,1,N);
> w=2*pi.*f; % Angular frequency
>
> %Function in the frequency domain
> alph=(1+i).*sqrt(w/2);
> gf=((1./(2*alph))).* exp(-alph.*2);
>
> %Function in the time domain
> gt = exp(-1./t)./(4*pi*t).^(1/2);
===================


I doubt you can use discrete transforms to transform functions like these with singularities at the origin.