Q1:

The initial and final value of $X(s)=\frac{s+14}{s^2+3s+15}$

Q2:

The impulse of the following RC system is?

Q3:

If H (s)=$\frac{5}{s^2+4s+5}$and step response is y(t)=A U(t)+B e–^2t cost u(t)- 2e^–ct sint u(t).Find  A,B,C?

Q4:

If$x(t)=10t^{-1}$. What will be x(j$\omega$).

Q5:

Find Fourier Transform of following signals

Q6:

The impulse response of the system is $h[n]=\left\{101\right\}$. What is the name of above filter.

Q7:

A sequence $x[n]={\left(\frac{1}{2}\right)}^{n}u[n]$and$y[n]=x^3[n]$. What is the value of $y(e^{j\omega })$at$\omega =\pi ?$

Q8:

$x[n]={\left(\frac{1}{2}\right)}^{-n}u[-n-1].$Fourier Transform of x[n] will be.

Q9:

Determine Fourier series coefficient of f(t)

Q10:

The second harmonic component of the periodic waveform given in the figure has amplitude of

Q11:

$F(x)=\left|\mathrm{Cos}x\right|:-\pi <x<\pi$then the Fourier series coefficient b₂ is:-

Q12:

Find the time domain whose exponential Fourier series coefficient $c_n=j\delta (n-1)-j\delta (n+1)+\delta (n-3)+\delta (n+3)$

Given ${\omega }_0=\pi .$

Q13:

The signum function is given by

$\mathrm{sgn}=\{\begin{array}{l}\frac{x}{\left|x\right|};x\ne 0\\ 0;x=0\end{array}$

The Fourier series expansion of sgn(Cos(t)) has

Q14:

Let x(t) be a periodic signal with time period, let $y(t)=x(t-t_0)+x(t+t_0)$ Fourier series coefficient at y(t) are denoted by b_k. If b_k = 0 for all odd k₁ then $t_0$ can be equal to

Q15:

The Fourier series expansion $f(t)=a_0+{\displaystyle \sum _{n=1}^{\infty }{a}_{n}cosn\omega t+b_{n}sinn\omega t}$ of the periodic signal shown will contain the following term:-

Q16:

The RMS value of a rectangular wave of period T having a value of +V for a duration $(0<t<T_1)$and -V for duration (T1<t<T) equals

Q17:

The impulse response g(t) of a system, G, is as shown in figure (a). What is the maximum value attained by the impulse response of two cascaded blocks of G as shown in figure (b)?

Q18:

Consider an LTI system with the transfer function$H(s)=\frac{1}{s(s+4)}$ if the input to the system is cos(3t) and the steady state output is A $\sin (3t+\alpha ),$ then the value of A is

Q19:

x(t) is non-zero only for -T_x< t < T_x, and similarly, y(t) is non – zero only for -T_y < t < T_y. Let z(t) be convolution of x(t) and  y(t). which one of the following statement is true?

Q20:

Two discrete time system with impulse response h₁[n]=$\delta$[n-1] and h₂[n]=$\delta$[n-2] are connected in cascade. The overall impulse response of the cascaded system is