PYQs Based Test - 03 : Signals & Systems

Which of the following statements is true about the two-sided Laplace transform?

The Fourier transform X(jω) of the signal

$\mathrm{x}(\mathrm{t})=\frac{\mathrm{t}}{(1+{\mathrm{t}}^2{)}^2}$

is _______.

Let x₁(t) = e${}^{-t}$ u(t) and x₂(t) = u(t) - u(t - 2), where u(⋅) denotes the unit step function.

If y(t) denotes the convolution of x₁(t) and x₂(t), then $\underset{t\to \infty }{\lim }y(t)=$ __________ (rounded off to one decimal place).

Consider a continuous-time system with input x(t) and output y(t) given by

y(t) = x(t)cos(t)

This system is

Let f(x) be a real, periodic function satisfying f(-x) = -f(x). The general form of its Fourier series representation would be