Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

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.....

share|improve this question
    
DT? What exactly do you mean? –  J. M. Sep 16 '11 at 7:14
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 7:18
1  
@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

1 Answer 1

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 $\omega_c$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.