List of top Signals and Systems Questions

A continuous real-valued signal $x(t)$ has finite positive energy and $x(t)=0,\ \forall\,t<0$. From the list below, select ALL signals whose continuous-time Fourier transform is purely imaginary.

The phase margin of the transfer function $G(s)=\dfrac{2(1-s)}{(1+s)^2}$ is ______ degrees (rounded off to the nearest integer).
The impulse response of an LTI system is $h(t)=\delta(t)+0.5\,\delta(t-4)$. If the input is $x(t)=\cos\!\left(\frac{7\pi}{4}t\right)$, the output is_____
The Laplace transform of the continuous-time signal $x(t)=e^{-3t}\,u(t-5)$ is ____, where $u(t)$ is the unit step.
Let $y(t)=x(4t)$, where $x(t)$ is a continuous–time periodic signal with fundamental period $100~\text{s}$. The fundamental period of $y(t)$ is _______ s (rounded off to the nearest integer).

Consider the discrete-time signal $x[n]=u[-n+5]-u[n+3]$, where $u[n]=\begin{cases}1,& n\ge 0\\0,&n<0\end{cases}$. The smallest $n$ for which $x[n]=0$ is ______.

A system has the transfer function $\dfrac{Y(s)}{X(s)}=\dfrac{s-\pi}{s+\pi}$. Let $u(t)$ be the unit–step function. The input $x(t)$ that results in a steady–state output $y(t)=\sin(\pi t)$ is _____.
A signal \(x(t) = 2\cos(180\pi t)\cos(60\pi t)\) is sampled at 200 Hz and then passed through an ideal low pass filter having cut-off frequency of 100 Hz. The maximum frequency present in the filtered signal in Hz is .......... (Round off to the nearest integer).
The period of the discrete-time signal \(x[n]\) described by the equation below is \(N =\) ..................... (Round off to the nearest integer). \[ x[n] = 1 + 3\sin\!\left(\frac{15\pi}{8}n + \frac{3\pi}{4}\right) - 5\sin\!\left(\frac{\pi}{3}n - \frac{\pi}{4}\right) \]
The discrete-time Fourier transform of a signal \(x[n]\) is \[ X(\Omega) = (1 + \cos \Omega) e^{-j\Omega} \] Consider that \(x_p[n]\) is a periodic signal of period \(N = 5\) such that \[ x_p[n] = x[n], \; n = 0,1,2, x_p[n] = 0, \; n=3,4 \] Note that \(x_p[n] = \sum_{k=0}^{N-1} a_k e^{j\frac{2\pi}{N}kn}\). The magnitude of the Fourier series coefficient \(a_3\) is ................ (Round off to 3 decimal places).
For the signals $x(t)$ and $y(t)$ shown in the figure, $z(t) = x(t) * y(t)$ is maximum at $t = T_{1$. Then $T_{1}$ in seconds is \underline{\hspace{1cm}} (Round off to the nearest integer).} \begin{center} \includegraphics[width=0.5\textwidth]{13.jpeg} \end{center}
Which of the following statement(s) is/are true?
The Z-transform of a discrete signal \(x[n]\) is \[ X(z) = \frac{4z}{\left(z-\tfrac{2}{3}\right)(z-3)}, \text{with ROC} = R. \] Which one of the following statements is true?
A continuous-time system that is initially at rest is described by: \[ \frac{dy(t)}{dt} + 3y(t) = 2x(t), \] where \(x(t)\) is the input voltage and \(y(t)\) is the output voltage. The impulse response of the system is:
The Fourier transform \(X(\omega)\) of the signal \(x(t)\) is given by \[ X(\omega) = \begin{cases} 1, & |\omega| < W_0
0, & |\omega| > W_0 \end{cases} \] Which one of the following statements is true?
For the block diagram shown in the figure, the transfer function \(\dfrac{Y(s)}{R(s)}\) is: \begin{center} \includegraphics[width=0.5\textwidth]{04.jpeg} \end{center}
Match List I with List II

List I (Message Signal)

List II (Related Units/Parameters)

A$4sin2\pi×5×10^3t-3 cos 2\pi ×8×10^3t  $I40 kHz
B$m(t)=2cos^2 2\pi×10^4t $II16 kHz
C$ m(t)=2sinc(2× 10^4 t) $III6 kHz
D$m(t)=5sinc^2(3x10^3t) $IV20 kHz
Choose the correct answer from the options given below:
The aliasing effect can be minimized by
A. selecting sampling frequency $w_s > 2w_m $
B. selecting sampling frequency $ w_s <2w_m $
C. selecting sampling frequency $w_s <w_m $ 
D. using anti-aliasing filter 
Choose the correct answer from the options given below.
Match List I with List II

List I (Signal)

List II (Fourier Transform)

A$ x(t-t_0)$ I$ \frac{dx(\omega)}{{d\omega}}$
B$ e^{j \omega_0 t} x(t) $II $ e^{j \omega t_0} X(\omega) $
C$ \frac{dx(t)}{{dt}}$III$ x(\omega-\omega_0)$ 
D$(-jt)x(t) $IV$j\omega X(\omega) $

Choose the correct answer from the options given below:
Given below are two statements:
Statement-I Fourier series of any periodic signal x(t) can only be obtained if x(t) is absolutely integrable over any period.
Statement-II : Fourier series of any periodic signal x(t) can only be obtained if x(t) has a finite number of discontinuities within finite time interval of t. 
In the light of the above statements, choose the correct answer from the options given below.
Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): A system is called causal if its output y(t) at an arbitrary time $t = t_0$ depends on only the input $ x(t)$ for $t≤t_0$.
Reason (R) : In a causal system, it is not possible to obtain an output before an input is applied to the system. In the light of the above statements,
In the light of the above statements, choose the correct answer from the options given below.
$H(s) = \frac1{ s^3+ As^2+Bs +5 } $ is the transfer function of a system. The system is stable for constraints
C(s) The noise transfer function $\frac{C(s)}{ N(S)}| _{R(S)=0} $of the given system is
The overall transfer function for the block diagram shown in figure is
The transfer function of two compensators is given as \(C_1= \frac{s+30}{ 30(s+1)}\) and\( C_2= \frac{30(1+s)}{ (30+s) }\) The correct statement is