1
$\begingroup$

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

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.....

  • 0
    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 $X(\cdot)$.2013-01-14

1 Answers 1

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 $\omega_c$.