Question

The input sin(20) is sampled at 20 ms intervals by using impulse train sampling: i. Construct the input and sampled signal spectra.

Answer 1

Let
`$x(t) = (\sin (20 \pi t))/(\pi t)$`

`$T_s = 20$` ms, so
`$f_s=(1)/(T_s)`

`$=(1)/(20)$`

= 0.05 kHz

`$f_s=50 $` Hz , ws =
`$2 \pi f_s = 100 \pi$` rad/s

We know that,

FT →
`$(\sin (20 \pi \omega))/(\pi \omega)$`

The sampled signal is :

`$XS(\omega) = (1)/(T_s) \sum_(k=- \infty)^(\infty)X (\omega-k\omega S)`

So,
`$XS(\omega) = (1)/(20 * 10^(-3)) \sum_(k=- \infty)^(\infty)X (\omega-100 k \pi)`

`$XS(\omega) = 50 \sum_(k=- \infty)^(\infty)X (\omega-100 k \pi)`