PYQs Based test 6: Signals & Systems

The causal signal with z-transform z ²(z - a) ⁻²is

(u[n] is the unit step signal)

Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) h(t) = y(t). Further, if |x(t)| |h(t)| = z(t), which of the following statements is true?

A cascade system having the impulse response {_1}≤ft( ) = ≤ft\{ {*20l 1, - 1\\ } \} and {_2}≤ft( ) = ≤ft\{ {*20l {1,1}\\ } \} is shown in the figure below, where symbol ↑ denotes the time origin.



The input sequence x(n) for which the cascade system produces an output sequence ≤ft( ) = ≤ft\{ {*20l {1,2,1,- 1,- 2,- 1}\\ } \} is

Let f(t) be a continuous-time signal and let F(ω) be its Fourier Transform defined by

$F\left(\omega \right)=\underset{-\infty }{\overset{\infty }{\int }}f\left(t\right)e^{-j\omega t}dt$

Define g(t) by

$g\left(t\right)=\underset{-\infty }{\overset{\infty }{\int }}F\left(u\right)e^{-jut}du$

What is the relationship between f(t) and g(t)?

Consider the two continuous-time signals defined below:

x_1≤ft( t ) = ≤ft\{ {*20c ≤ft| t |, - 1 ≤ t ≤ 1 \\ 0, otherwise ,} .x_2≤ft( t ) = ≤ft\{ {*20c 1 - ≤ft| t |, - 1 ≤ t ≤ 1 \\ 0, otherwise } .

These signals are sampled with a sampling period of T = 0.25 seconds to obtain discrete time signals x₁[n] and x₂[n], respectively. Which one of the following statements is true?