Need help to solve FFT and IFFT by mathematica

[akter]

Homework Statement

I want to solve FFT and IFFT in the same problem. My function is Exp[2*(1 + I*c)*T^2].

For FFT, I used the following code:

ClearAll["Global'*"]
c = 0;
f[t_] = Exp[-(1 + I*c)*2*t^2];
sampleTime = .01;
data1 = Table[f[t], {t, -5, 5, sampleTime}];
freq1 = Fourier[data1];

now I need to do IFFT of ( freq1*Exp[-0.5*(z/(1 - I*v))] ) function.
Before perform IFFT, i converted Exp[-0.5*(z/(1 - I*v))] into frequency data as same matrix of freq1. Here is my code:

s = Exp[-0.5*(z/(1 - I*v))];
data2 = Table[s, {v, 0, 2000*Pi, 2*Pi}];

Then i performed IFFT by

freq2 = InverseFourier[data2*freq1];

Homework Equations

Now i am confused whether my IFFT solution way is correct or not. I got idea of sampling frequency , Table[s, {v, 0, 2200*Pi, 2*Pi}] from some Matlab tutorial.Is there any another way I can calculate IFFT for my function?

The Attempt at a Solution

Finally i want to plot (Abs[freq2])^2 with respect to time for different value of z.
z=1;
ListLinePlot[(Abs[freq2]*Abs[freq2]), PlotRange -> Full]

But i got the curve in terms of data value 0 to 1000.

How can i get the curve with respect to time now??
Thanks,
Akter

 

[mark726]

Hi Akter,

Your approach for solving FFT and IFFT in the same problem seems correct. However, there are a few suggestions I have for you:

1. Instead of using a fixed value for c (in your example, c=0), you can try using a range of values and see how the FFT and IFFT results vary. This will give you a better understanding of the frequency and time domain relationships.

2. In your code for calculating data2, you have used a fixed range for v (0 to 2000*Pi). Instead, you can use the same range of values as you did for data1 (from -5 to 5 with a sample time of 0.01). This will ensure that the frequency data is consistent with the time data.

3. To plot the results with respect to time, you can use the following code:

time = Table[t, {t, -5, 5, sampleTime}];
ListLinePlot[Transpose[{time, Abs[freq2]^2}], PlotRange -> Full]

This will give you a plot with time on the x-axis and the square of the absolute values of frequency on the y-axis.

I hope this helps. Good luck with your problem!