Question

Consider the signal s(t) shown in the figure below:

If this signal is applied to its matched filter, then the value of filter output signal at T=3 sec will be _____V.

• A. 4

Answer 1

The correct option is A 4
Impulse response of the filter matched to the signal s(t) will be

$h\left(t\right)=s(T-t);T=2\text{sec}$




$\text{So,}h\left(t\right)=2\left[u\right(t)-u(t-2\left)\right]$

$s\left(t\right)=2\left[u\right(t)-u(t-2\left)\right]$

$\text{Output signal,}y\left(t\right)=s\left(t\right)\ast h\left(t\right)=4\left[r\right(t)-r(t-2)-r(t-2)+r(t-4\left)\right]$

$=4\left[r\right(t)-2r(t-2)+r(t-4\left)\right]$

By plotting y(t), we get,

So, the value of y(t) at t=3 sec is 4 V