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Signals and Systems

28 Questions
GATE→2026→Signals and Systems→Signals and Systems
Q1
MCQ[1 Mark]
A square wave signal of frequency 20 kHz is passed through an ideal low-pass filter with cut-off frequency of 21 kHz. The output signal is a
GATE→2026→Signals and Systems→Signals and Systems
Q2
MCQ[1 Mark]
Given x(t)=4sin⁡(15πt)+7cos⁡(4πt)x(t) = 4 \sin(15\pi t) + 7 \cos(4\pi t), where t is in seconds. The fundamental period of x(t)x(t) is
GATE→2026→Signals and Systems→Signals and Systems
Q3
MCQ[2 Marks]
A signal x(t)x(t) is shown below. The plot of y(t)=1−x(4−t)y(t) = 1 - x(4-t) is shown in
Figure for Question 3
GATE→2026→Signals and Systems→Signals and Systems
Q4
MCQ[2 Marks]
In the table shown below, List-I are the system responses to input x(t)x(t) and List-II are the system properties. The correct matching is
GATE→2026→Signals and Systems→Signals and Systems
Q5
MCQ[2 Marks]
Given two signals: x(t)=u(t−2)−u(t−3)x(t) = u(t-2) - u(t-3), and y(t)=e−4tu(t)y(t) = e^{-4t}u(t). If z(t)=x(t)∗y(t)z(t) = x(t) * y(t), then Z(s) is
GATE→2025→Signals and Systems→Signals and Systems
Q6
MCQ[1 Mark]
Let a continuous-time signal be x(t)=ej9t+ej5tx(t) = e^{j9t} + e^{j5t}, where j=−1j = \sqrt{-1} and t is in seconds. The fundamental period of magnitude of x(t)x(t), in seconds, is
GATE→2025→Signals and Systems→Signals and Systems
Q7
MCQ[2 Marks]
Let y[n]=1αy[n−1]+x[n]y[n] = \frac{1}{\alpha}y[n-1] + x[n], where α>1\alpha > 1 and real, represent a difference equation of a causal discrete-time linear time invariant system. The system is initially at rest. If x[n]=δ[n−p]x[n] = \delta[n-p] where p>10p > 10, the value of y[p+1]y[p+1] is
Figure for Question 7
GATE→2025→Signals and Systems→Signals and Systems
Q8
MCQ[2 Marks]
Let f(t)f(t) and g(t)g(t) represent continuous-time real-valued signals. If h(t)h(t) denotes cross-correlation between f(t)f(t) and g(−t)g(-t), its continuous-time Fourier transform H(jω)H(j\omega) equals
GATE→2025→Signals and Systems→Signals and Systems
Q9
MSQ[2 Marks]
Choose the eigenfunction(s) of stable linear time-invariant continuous-time systems from the following options.
GATE→2025→Signals and Systems→Signals and Systems
Q10
NAT[2 Marks]
Let X(ejω)X(e^{j\omega}) represent the discrete time Fourier transform of a 4-length sequence x[n]...x[n]... The value of y[0]y[0] is (in integer).
GATE→2024→Signals and Systems→Signals and Systems
Q11
MCQ[1 Mark]
A discrete-time sequence is given by x[n]=[1,2,3,4]x[n] = [1, 2, 3, 4] for 0≤n≤30 \le n \le 3. The zero lag auto-correlation value of x[n]x[n] is
GATE→2024→Signals and Systems→Signals and Systems
Q12
NAT[1 Mark]
Consider a filter defined by the difference equation y[n]−0.5y[n−2]=ax[n−4]y[n] - 0.5y[n-2] = a x[n-4]... The value of a is (rounded off to two decimal places).
GATE→2024→Signals and Systems→Signals and Systems
Q13
NAT[1 Mark]
The number of complex multiplications required for computing a 16-point DFT using the decimation-in-time radix-2 FFT is (in integer).
GATE→2024→Signals and Systems→Signals and Systems
Q14
NAT[1 Mark]
The Nyquist sampling frequency for x(t)=10sin⁡2(200πt)x(t) = 10 \sin^{2}(200\pi t) is Hz (rounded off to nearest integer).
GATE→2024→Signals and Systems→Signals and Systems
Q15
MCQ[2 Marks]
Consider a discrete-time sequence x[n]={(0.2)n,0≤n≤70,otherwisex[n] = \begin{cases} (0.2)^{n}, & 0 \le n \le 7 \\ 0, & \text{otherwise} \end{cases}. The region of convergence of X(z)X(z), the z-transform of x[n]x[n] consists of
GATE→2024→Signals and Systems→Signals and Systems
Q16
MCQ[2 Marks]
Laplace transform of a signal x(t)x(t) is X(s)=1s2+13s+42X(s) = \frac{1}{s^{2} + 13s + 42}. Let u(t)u(t) be the unit step function. Choose the signal x(t)x(t) from the following options if the region of convergence is −7<Re{s}<−6-7 < \text{Re}\{s\} < -6.
GATE→2024→Signals and Systems→Signals and Systems
Q17
NAT[2 Marks]
The 4-point DFTs of two sequences x[n]x[n] and y[n]y[n]... the value of z[0]z[0] is (rounded off to nearest integer).
GATE→2023→Signals and Systems→Signals and Systems
Q18
MCQ[1 Mark]
A system has the transfer-function Y(s)X(s)=s−πs+π\frac{Y(s)}{X(s)} = \frac{s - \pi}{s + \pi}. Let u(t)u(t) be the unit-step function. The input x(t)x(t) that results in a steady-state output y(t)=sin⁡(πt)y(t) = \sin(\pi t) is
GATE→2023→Signals and Systems→Signals and Systems
Q19
NAT[1 Mark]
Consider the discrete-time signal x[n]=u[−n+5]−u[n+3]...x[n] = u[-n+5] - u[n+3]... The smallest n for which x[n]=0x[n] = 0 is
GATE→2023→Signals and Systems→Signals and Systems
Q20
NAT[1 Mark]
Let y(t)=x(4t)y(t) = x(4t), where x(t)x(t) is a continuous-time periodic signal with fundamental period of 100 s. The fundamental period of y(t)y(t) is s (rounded off to the nearest integer).
GATE→2023→Signals and Systems→Signals and Systems
Q21
MCQ[2 Marks]
The impulse response of an LTI system is h(t)=δ(t)+0.5δ(t−4)h(t) = \delta(t) + 0.5\delta(t-4)... If the input signal x(t)=cos⁡(7π4t)x(t) = \cos(\frac{7\pi}{4}t), the output is
GATE→2023→Signals and Systems→Signals and Systems
Q22
MCQ[2 Marks]
The Laplace transform of the continuous-time signal x(t)=e−3tu(t−5)x(t) = e^{-3t}u(t-5) is
GATE→2023→Signals and Systems→Signals and Systems
Q23
MCQ[2 Marks]
A continuous real-valued signal x(t)x(t) has finite positive energy and x(t)=0,∀t<0x(t) = 0, \forall t < 0. From the list given below, select ALL the signals whose continuous-time Fourier transform is purely imaginary.
GATE→2022→Signals and Systems→Signals and Systems
Q24
MCQ[1 Mark]
The input x(t)x(t) to a system is related to its output y(t)y(t) as dy(t)dt+y(t)=3x(t−3)u(t−3)\frac{dy(t)}{dt} + y(t) = 3x(t-3)u(t-3)... The transfer function of this system is
GATE→2022→Signals and Systems→Signals and Systems
Q25
MCQ[1 Mark]
The output of a system y(t)y(t) is related to its input x(t)x(t) according to the relation y(t)=x(t)sin⁡(2πt)y(t) = x(t)\sin(2\pi t). This system is
GATE→2022→Signals and Systems→Signals and Systems
Q26
MCQ[1 Mark]
A signal x(t)x(t) is band-limited between 100 Hz and 200 Hz. A signal y(t)y(t) is related to x(t)x(t) as follows: y(t)=x(2t−5)y(t) = x(2t-5). The statement that is always true is
GATE→2022→Signals and Systems→Signals and Systems
Q27
MCQ[2 Marks]
Consider the transfer function Hc(s)=1(s+1)(s+3)H_{c}(s) = \frac{1}{(s+1)(s+3)}. Bilinear transformation with a sampling period of 0.1 s is employed to obtain the discrete-time transfer function Hd(z)H_{d}(z). Then Hd(z)H_{d}(z) is
GATE→2022→Signals and Systems→Signals and Systems
Q28
MCQ[2 Marks]
The signal x(t)=(t−1)2u(t−1)x(t) = (t-1)^{2}u(t-1), where u(t)u(t) is the unit-step function, has the Laplace transform X(s)X(s). The value of X(1)X(1) is