1. ## Fourier transform help

Hi,

I have a problem with the calculation of DFT(discrete fourier transform) of the signal x(n) above. I've attached the signal x(n) and also the definition of DFT I am using.
So, How can I calculate Xk ,the dft, of this signal?

This is what I did.

for k=0,1,2...N-1

Can you tell me if this is right and also help me to sketch the magnitude of Xk as a function of k in the range of 0...N-1 ?

Nikolas

2. Originally Posted by tsebamm

Hi,

I have a problem with the calculation of DFT(discrete fourier transform) of the signal x(n) above. I've attached the signal x(n) and also the definition of DFT I am using.
So, How can I calculate Xk ,the dft, of this signal?

This is what I did.

for k=0,1,2...N-1

Can you tell me if this is right and also help me to sketch the magnitude of Xk as a function of k in the range of 0...N-1 ?

Nikolas
Could you repost this with slightly bigger graphics that are easier to read, please.

CB

3. Originally Posted by tsebamm

Hi,

I have a problem with the calculation of DFT(discrete fourier transform) of the signal x(n) above. I've attached the signal x(n) and also the definition of DFT I am using.
So, How can I calculate Xk ,the dft, of this signal?

This is what I did.

for k=0,1,2...N-1

Can you tell me if this is right and also help me to sketch the magnitude of Xk as a function of k in the range of 0...N-1 ?

Nikolas
Applying the DFT definition is...

$\displaystyle \displaystyle X_{k} = \sum_{n=0}^{N-1} x(n)\ e^{-j 2 \pi \frac{k n}{N}} = \frac{1}{2}\ \sum_{n=0}^{1} e^{-j 2 \pi \frac{k n}{N}}= \frac{1}{2}\ (1+ e^{-j 2 \pi \frac{k}{N}})$

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

P.S. I suggest tsebann to learn Latex!...

4. Originally Posted by chisigma
Applying the DFT definition is...

$\displaystyle \displaystyle X_{k} = \sum_{n=0}^{N-1} x(n)\ e^{-j 2 \pi \frac{k n}{N}} = \frac{1}{2}\ \sum_{n=0}^{1} e^{-j 2 \pi \frac{k n}{N}}= \frac{1}{2}\ (1+ e^{-j 2 \pi \frac{k}{N}})$

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

P.S. I suggest tsebann to learn Latex!...
Thanks both of you! You are right, when I find some time I will try to learn Latex.
I think chisigma gave me the answer I want. This is what I did in the blur image. I was just not sure if I have had to take some values for N! The question of the excersise is : "Calculate Xk, the dft of the signal" . So, I think that it is ok.
Thanks again

Regards,
Nikolas

5. Hi again and sorry for the double posting.
I am trying to sketch the magnitude of Xk that we found above as a function of k in the range 0...N-1.
Should I take the equation ? But how can I use it here?

I have made an attempt. I take values for k. (0,1,2,3...N-1) but I don't know what to do with N. I have an idea to take conditions for it.If it is even or odd but I can not conclude something with that.
Can anyone help me with that?
i have checked a lot of stuff via the internet.I would appreciate if you give me a solution with that and a small explanation.

Oh, N is an integer of course!