Please help me with Discrete Fourier Transform

[al289]

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.

 

[msp4u4ever]

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