Discrete Fourier transform question

[thereddy]

Summary:: Discrete Fourier transform exam question

Hi there, I'm not really sure how to do this question at all. Any help would be appreciated.

 

[BvU]

hello reddy, !

Unfortunately (well...), PF isn't a magical box where you dump problems and receive a solution on a silver platter.

Please read the https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

they tell you that you must post an attempt at solution before we are allowed to assist (i.e. not do the work for you) with useful hints and guiding questions !

 

[BvU]

Looked at your exercise. Not for the faint-hearted.

My advice: if you don't know where to start, start where your knowing is. What do you know about sampling, DFT, etc. ? Can we make it easier with just $f(t) = \sin(2\pi f_1 t)\$ ?

 

[BvU]

Are you still here ?

 

[DrClaude]

Looked at your exercise. Not for the faint-hearted.

Depends on what is covered in the course. I would expect my students to be able to answer this question without too much thought, including even the complex phase of the frequency components.

 

[Delta2]

Depends on what is covered in the course. I would expect my students to be able to answer this question without too much thought, including even the complex phase of the frequency components.

By looking at the function and the sampling rate i suppose we can conclude which going to be the main frequencies present in the DFT, but is it really possible to know the exact magnitude and phase of the DFT without actually doing the DFT ?

 

[DrClaude]

By looking at the function and the sampling rate i suppose we can conclude which going to be the main frequencies present in the DFT, but is it really possible to know the exact magnitude and phase of the DFT without actually doing the DFT ?

With a $y(t)$ such as that given in the OP, yes. However, I cannot say more for now as it would help the OP too much.