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Please help me with Discrete Fourier Transform

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al289

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Hallo,

I'm learning DSP myself with the book Understanding DSP (Richard G. Lyons). I am stuck with DFT, I don't understand how they can plot some following figures.
Could anyone please help to explain how, and which equation did they use to plot those figures
Thank you very much.
DFT 1.pngDFT 2.png
dft3.png
 

msp4u4ever

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I can't exactly help you in plotting those graphs but the following may help you:

DFT spectrum is discrete in nature whereas the DTFT spectrum is continuous and DFT spectrum can be obtained by sampling the DTFT spectrum at regular intervals

DTFT: X(omega) = Sigma x[n].e^(-j*omega*n)
DFT : X(k) = Sigma x[n].e(-j*2*pi*k*n/N)

therefore omega = 2*pi*k*n/N which gives k = [omega/(2*pi)]*N
 

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