EE-406: Problem Set 3. Q3

Hello,

The following figure shows the spectrum of

$|X(\omega)|$ and

$|H(\omega)|$ .

Let us observe for example

$|H(\omega)|$ , you see that it is zero for frequencies below

$-\frac{\pi}{5}$ or above

$\frac{\pi}{5}$ .

This is called an ideal low pass filter.

Its cut-off frequency is

$\omega_c$ =

$\frac{\pi}{5}$ here. Everything is set to zero above this cut-off frequency.

Note if you filter a signal x(t) with h(t). It ends up multiplying in the Fourier domain, hence we get the final answer.

Let me know if it is still unclear

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