$$x[n] = \frac{3\sin{(3\pi\frac{n}{4})}}{\pi n}$$
What is the Discrete Time Fourier Transform $X(e^{jw})$ of $x[n]$?
Thanks.
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. ain't a mathematician Sep 16 '11 at 07:14
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1@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 07:18
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1@Gerben : I think it is DTFT but not DFT. – Sep 16 '11 at 07:25
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I'm asking because OP should have supplied what formula he's supposed to use, sign/normalization and all... – J. M. ain't a mathematician Sep 16 '11 at 07:39
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I need to plot a graph of $X(e^{jw})$ for the sinc function x[n]. – zingsi123 Sep 16 '11 at 09:15
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@zingsi123 You should consider transferring this question to the newly established site dsp.stackexchange.com for digital signal processing. – Dilip Sarwate Sep 17 '11 at 00:56
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The $x(n)$ $\ (n\in{\mathbb Z})$ are the Fourier coefficients of a certain $2\pi$-periodic function $X(\cdot)$. The problem consists in finding an expression for $X(\cdot)$. – Christian Blatter Jan 14 '13 at 21:01
