FFT Problem Solved by Mathematica | Exercise 2

[gazi habiba]

Hi,
I have to solve a FFT problem by mathematica.I have attached my problem(exercise 2) here. I do not understand fft algorithm well.I also try to solve it by mathematica but mathematica can not solve this by forier transform directly.It will be great if anyone help me to solve this problem.

 

[gazi habiba]

Hi,
I have to solve a FFT problem by mathematica.I have attached my problem(exercise 2) here. I do not understand fft algorithm well.I also try to solve it by mathematica but mathematica can not solve this by Fourier transform directly.It will be great if anyone help me to solve this problem.

 

[K^2]

You do not need to understand FFT algorithm. You only need to understand relation betwen Discrete Fourier Transform (DFT) and Continuous Fourier Transform to understand how a numerical model using DFT approximates the analytic form with Fourier Transformed functions.

Once you understand that, you can simply use Mathematica's built in function to apply FFT to compute DFT of arrays you supply. Don't worry too much about HOW Mathematica does it. You just need to know what the results mean.

Edit: Just to clarify, DFT is a vector transformation. It's the set of rules on how to take a vector and produce a transformed vector. FFT is a specific numerical method for making this transformation really fast. It's a very interesting topic, but you usually don't need to know how it actually happens.

 

[gazi habiba]

Thanks for your reply.
I read some books for understand FFT and DFT.It is not clear to me still now.May be i am not math or physics student for that reason i cannot understand.I can not go forward my thesis without solving this. Is it possible to explain me with a simple function like f(t)= Exp[-t^2] instead of my function.

thanks,
Gazi