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Math Help - Fourier transform help

  1. #1
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    Fourier transform help

    Fourier transform help-dft.png


    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.

    Fourier transform help-dft2.jpg

    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 ?

    Thanks in advance,
    Nikolas
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by tsebamm View Post
    Click image for larger version. 

Name:	dft.png 
Views:	62 
Size:	4.3 KB 
ID:	19615


    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.

    Click image for larger version. 

Name:	dft2.jpg 
Views:	65 
Size:	8.4 KB 
ID:	19617

    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 ?

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

    CB
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  3. #3
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by tsebamm View Post
    Click image for larger version. 

Name:	dft.png 
Views:	62 
Size:	4.3 KB 
ID:	19615


    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.

    Click image for larger version. 

Name:	dft2.jpg 
Views:	65 
Size:	8.4 KB 
ID:	19617

    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 ?

    Thanks in advance,
    Nikolas
    Applying the DFT definition is...

    \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

    \chi \sigma

    P.S. I suggest tsebann to learn Latex!...
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  4. #4
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    Quote Originally Posted by chisigma View Post
    Applying the DFT definition is...

    \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

    \chi \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
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  5. #5
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    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!
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