Signal and Systems GATE Questions

Practising previous years’ GATE Questions papers are the most widely used way to prepare for the GATE Exam. Candidates can practise, analyse and understand concepts while solving them. It helps students strengthen their time management skills. We have attempted to compile, here in this article, a collection of GATE Questions on Signal and Systems.

Candidates are urged to practise these Signal and Systems GATE previous years’ questions to get the best results. Signal and Systems is an important topic in the GATE question papers, and solving these questions will help the candidates to prepare more proficiently for the ECE GATE exams. Therefore, candidates can find the GATE Questions for Signal and Systems in this article to solve and practise well before the exams. They can also refer to these GATE previous year question papers and start preparing for the exams.

GATE Questions on Signal and Systems

1. If the Laplace transform of a signal y(t) is
   \(\begin{array}{l}Y(s) = \frac{1}{s(s-1)}\end{array} \)
   , then its final value is ______.

(GATE ECE 2007)

1. -1
2. 0
3. 1
4. Unbounded

Answer (d)

2. The Laplace transform of i(t) tends to
\(\begin{array}{l}I(s) = \frac{2}{s(1+s)}\end{array} \)

As t → ∞, the value of i(t) tends to _______.

(GATE ECE 2007)

1. 0
2. 1
3. 2
4. ∞

Answer (c)

3. The final value theorem is used to find the _______.

(GATE ECE 1995)

1. Steady-state value of the system output
2. Initial value of the system output
3. Transient behaviour of the system output
4. None of these

Answer (a)

4. The laplace transform of a unit ramp function starting at t=a, is ______.

(GATE ECE 1994)

1. \(\begin{array}{l}\frac{1}{(s+a)^{2}}\end{array} \)
2. \(\begin{array}{l}\frac{e^{-as}}{(s+a)^{2}}\end{array} \)
3. \(\begin{array}{l}\frac{e^{-as}}{(s)^{2}}\end{array} \)
4. \(\begin{array}{l}\frac{a}{s^{2}}\end{array} \)

Answer (c)

5. An LTI system with unit sample response

h(n)=5δ[n]−7δ[n−1]+7δ[n−3]−5δ[n−4] is a _______.

(GATE ECE 2017 Set 2)

1. Low pass filter
2. High pass filter
3. Band pass filter
4. Band stop filter

Answer (C)

6. A system is defined by its impulse response h(n)=2ⁿu(n−2). The system is _______.

(GATE ECE 2011)

1. Stable and casual
2. Casual but not stable
3. Stable but not casual
4. Unstable and non-casual

Answer (b)

7. A Hilbert transformer is a ______.

(GATE ECE 2007)

1. Nonlinear system
2. Non-casual system
3. Time-varying system
4. Low-pass system

Answer (b)

8. Match the following and choose the correct combination.

GROUP 1

E- continuous and aperiodic signal

F- continuous and periodic signal

G- discrete and aperiodic signal

H- discrete and periodic signal

Group 2

1- Fourier representation is continuous and aperiodic

2- Fourier representation is discrete and aperiodic

3- Fourier representation is continuous and periodic

4- Fourier representation is discrete and periodic

(GATE ECE 2005)

1. E-3, F-2, G-4, H-1
2. E-1, F-3, G-2, H-4
3. E-1, F-2, G-3, H-4
4. E-2, F-1, G-4, H-3

Answer (c)

9. A fully charged mobile phone with a 12 V battery is good for a 10-minute talk time. Assume that, during the talk-time, the battery delivers a constant current of 2 A, and its voltage drops linearly from 12 V to 10 V, as shown in the figure. How much energy does the battery deliver during this talk-time?

(GATE ECE 2009)



1. 220 J
2. 12 kJ
3. 13.2 kJ
4. 14.4 kJ

Answer (c)

10. For a periodic signal v(t) = 30 sin 100t + 10cos 300t + 6sin (500t+π/4), the fundamental frequency in rad/s is __________.

(GATE ECE 2013)

1. 100
2. 300
3. 500
4. 1500

Answer (a)

11. The ACF of a rectangular pulse of duration T is _______.

(GATE ECE 1998)

1. A rectangular pulse of duration T
2. A rectangular pulse of duration 2T
3. A triangular pulse of duration T
4. A triangular pulse of duration 2T

Answer (d)

12. Consider the following statements for continuous-time linear time-invariant (LTI) systems.

I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.

II. There is no causal and BIBO stable system with a pole in the right half of the complex plane.

Which one among the following is correct?

(GATE ECE 2017 Set 1)

1. Both I and II are true
2. Both I and II are not true
3. Only I is true
4. Only II is true

Answer (d)

13. The impulse response of an LTI system can be obtained by __________.

(GATE ECE 2015 Set 3)

1. Differentiating the unit ramp response
2. Differentiating the unit response
3. Integrating the unit ramp response
4. Integrating the unit step response

Answer (b)

14. Two systems with impulse responses h₁(t) and h₂(t) are connected in a cascade. Then the overall impulse response of the cascaded system is given by ______.

(GATE ECE 2013)

1. Product of h₁(t) and h₂(t)
2. Sum of h₁(t) and h₂(t)
3. Convolution of h₁(t) and h₂(t)
4. Subtraction of h₁(t) and h₂(t)

Answer (c)

15. The input and output of a continuous system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system?

(GATE ECE 2008)

1. y(t) = x(t-2) + x(t+4)
2. y(t) = (t-4)x(t+1)
3. y(t) = (t+4)x(t-1)
4. y(t) = (t+5)x(t+5)

Answer (c)