PYQs Based Test - 04 : Signals & Systems

The output y[n] of a discrete-time system for an input x[n] is

$y\left[n\right]=\underset{-\infty \le k\le n}{\max }\left|x\left[k\right]\right|$

The unit impulse response of the system is

Consider the parallel combination of two LTI systems shown in the figure.



The impulse response of the systems are

h₁(t) = 2δ(t + 2) - 3δ(t + 1)

h₂(t) = δ(t - 2).

If the input x(t) is a unit step signal, then the energy of y(t) is ___________ .

A discrete-time all-pass system has two of its poles at 0.25∠0° and 2∠30°. Which one of the following statement about the system is TRUE?

For an all pass system $H\left(z\right)=\frac{z^{-1}-b}{1-a{z}^{-1}}$ If Rₑ(a)≠0, I${}_m$ (a)≠0, then b equals.

A system with transfer function $G\left(s\right)=\frac{1}{\left(s+1\right)\left(s+a\right)},a>0$ is subjected to an input 5 cos 3t. The steady-state output of the system is $\frac{1}{\sqrt{10}}\cos \left(3t-1.892\right)$. The value of a is