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$$x[n] = \frac{3\sin{(3\pi\frac{n}{4})}}{\pi n}$$

What is the Discrete Time Fourier Transform $X(e^{jw})$ of $x[n]$?


I need to plot a graph of $X(e^{jw})$ for the sinc function x[n]. I know it is a rectangular waveform.....

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DT? What exactly do you mean? – J. M. Sep 16 '11 at 7:14
@J. M.: I'm guessing it's the discrete FT, i.e. for $N$ points $\{f(k) | k = 0,\ldots,N-1 \},$, you get $$f(n) \mapsto \sum_k e^{-2\pi i nk/N} f(k).$$ – Gerben Sep 16 '11 at 7:18
@Gerben : I think it is DTFT but not DFT. – user13838 Sep 16 '11 at 7:25
I'm asking because OP should have supplied what formula he's supposed to use, sign/normalization and all... – J. M. Sep 16 '11 at 7:39
I need to plot a graph of $X(e^{jw})$ for the sinc function x[n]. – zingsi123 Sep 16 '11 at 9:15

Note that $$\dfrac{\sin \omega_c n}{\pi n}\Longleftrightarrow \text{rect}\left(\dfrac{\omega}{2\omega_c}\right)$$ which is a rectangular function from $-\omega_c$ to $\omega_c$.

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