PYQs Based Test - 03 : Signals and Systems

The Fourier transform of a signal x(t), denoted by X(jω), is shown in the figure.



Let y(t) = x(t) + e${}^{jt}$ x(t). The value of Fourier transforms of y(t) evaluated at the angular frequency ω = 0.5 rad/s is

The Laplace transform of a causal signal y(t) is $y\left(s\right)=\frac{s+2}{s+6}$. The value of the signal y(t) at t = 0.1s is ______ units.

For the periodic signal x(t) shown below with period T = 8s, the power in the 10${}^{th}$ harmonic is

Consider a periodic signal x(t) as shown below:



It has a Fourier series representation

$x\left(t\right)=\sum _{k=-\infty }^{\infty }{a}_k{e}^{j\left(\frac{2\pi }{T}\right)kt}$

Which one of the following statements is TRUE?

f(x), shown in the figure is represented by $f\left(x\right)=a_0+\sum _{n=1}^{\infty }\left(a_n\cos \left(nx\right)+b_n\sin \left(nx\right)\right)$

The value of a₀ is