Inverse Fourier Transform using MATLAB

[orstats]

I would like to do an inverse Fourier transform using MATLAB's IFFT. I am confused by MATLAB'S single input of X for its IFFT function. Has anyone had experience using MATLAB for these tranforms?

I would like to do an inversion of Fourier transform for my function y(iw) at some value real value z. I am confused at how to specify my function y(iw) and z in MATLAB's IFFT(X).

In the continuous setting, the inverse Fourier transform, ift(), would be

ift(z) = 1/2pi * Integral [ e^(-iwz) y(iw) dw ]

In other words, I specify z and specify y, which is only a function of w which I am integrating over. But how do I do this using MATLAB's IFFT, when it only takes an input X...

Does anyone have any recommendations of computationally solving these integrals for vectors of z and known analytical expression of y(iw)?

 

[astrosona]

HI!

wahoooooooooo, the similar problem took couple days for me couple weeks ago! and i was so frustrated in that time...

Because this is not a physics problem and you are not suppose to think what Matlab designers liked to use as command! i think i am allowed to just copy all my work for you so you can learn the right commands to use ;)

sorry that i don't have time to look cerefully to your problem (i am working on some other Matlab programs! ) but i am sure the below program will help you :

----------------------------------------

% problem set 3
%
% the function f and it's Fourier (inverse Fourier in Matlab) transform with diffrent methods
% wm = w(mn)
% W = w
% T = Life time
% tn= time variable
% f in my funtion

%part a:

tn=[0:0.01:30];
T=1/(0.3);
wm=4;
f=exp((-i.*wm.*tn)-(tn/T));
plot(tn,real(f),tn,imag(f))
%part b
%In this part I had found the Fourier transition analetically myself and i
%will plot the real and imaginary parts seperated

T=1/(0.3);
wm=4;
w=[0:0.1:10];

for(i=1:length(w))
%the real part of Fourier transform of f
R(i)=(1/T) /( (2*pi)*(((w(i)-wm)^2)+(1/(T^2))));
%%the imaginary part of Fourier transform of f
I(i)=(1/(2*pi))*((w(i)-wm)/(((w(i)-wm).^2)+(1/(T.^2))));
end

hold
plot(w,R,w,I)
plot(w,abs(R).^2,w,abs(I).^2)%part c
%In this part i have to let MatLab to find the Fourier transformation and
%plot the real and imaginary parts and comper them with the part b which
%was the same problem but it was anatletically. the poin is is can make my
%spacing farther in this part to see the diffrence more, i.e. in case of N=50

N=500;
Tmax=50;
T=1/(0.3);
wm=4;

for (p=1:N)
tn(p)=(Tmax/N)*p;
wk(p)=((2*pi)/Tmax)*p;
f(p)=exp(-j*wm*tn(p)) * exp(-tn(p)/T);
% j is the imajinary element which is mostly defined by i but Matlab
% has problem with i so we wrote j and Matlab jot it! ;)
end

F=ifft(f);
%size(F)
%size(wk)
%plot(tn,real(f))
hold
plot(wk,real(F),wk,imag(F))
plot(wk,abs(real(F)).^2,wk,abs(imag(F)).^2)---------------------------------

good luck! ;)

 

[astrosona]

I need to know how can i plot different figures in different windows and have all those windows open separately simultaneously? any idea?

 

[orstats]

It depends on what the aim. If it is simply to view them at once, without using MATLAB, you can simply insert the n figures in n panels in an editor, such as MS Word.

 

[orstats]

Btw, thank you for your sample code. You may also find this offering by Mathematica interesting:

website slash slash
reference.wolfram.com/mathematica/FourierSeries/tutorial/FourierSeries.html

Your expression f() for which you are taking the Fourier transform, you may express as an input for their Fourier Transform function. I wonder what were MATLAB's challenges in conceptualizing and implement this...?

 

[astrosona]

cool! well...! i don't know! i have to look for it... ;)