GATE EC||SIGNALS & SYSTEMS ||BASIC OF SIGNALS & SYSTEMS|| PYQS(2000-2025)

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Question 1

(GATE 2019 || EC || PYQ || NAT || 1 MARKS)

Question 2

Let the input be u and the output be y of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:

(GATE 2018 || EC || [PYQ || MCQ || 1 MARKS)

y = au + b, b ≠ 0
y = au

Question 3

Consider a single input single output discrete-time system with x[n] as input y[n] as output, where the two are related as

Which one of the following statements is true about the systems?

(GATE 2017 || EC || PYQ || MCQ || 1 MARKS)

It is causal and stable.
It is causal but not stable.
It is not causal but stable.
It is neither causal nor stable.

Question 4

The input x(t) and output y(t) of a system are related as

The system is

(GATE 2012 || EC || PYQ || MCQ || 2 MARKS)

time-invariant and stable.
stable and not time-invariant.
time-invariant and not stable.
not time-invariant and not stable.

Question 5

Let x(t) be the input and y(t) be the output of a continuous time system. Match the system properties P₁, P₂ and P₃ with system relations R₁, R₂, R₃, R₄.

Properties

P₁: Linear but NOT time-invariant

P₂: Time-invariant but NOT linear

P₃: Linear and time-invariant

Relations

R₁: y(t) = t²x(t)

R₂: y(t) = t|x(t)|

R₃: y(t) = |x(t)|

R₄: y(t) = x(t – 5)

(GATE 2008 || EC || PYQ || MCQ || 2 MARKS)

(P₁, R₁), (P₂, R₃), (P₃, R₄).
(P₁, R₂), (P₂, R₃), (P₃, R₄).
(P₁, R₃), (P₂, R₁), (P₃, R₂).
(P₁, R₁), (P₂, R₂), (P₃, R₃)

Question 6

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

(GATE 2008 || EC || PYQ || MCQ || 1 MARKS)

y(t) = x(t – 2) + x(t + 4)
y(t) = (t – 4)x(t + 1)
y(t) = (t + 4)x(t – 1)
y(t) = (t + 5)x(t + 5)

Question 7

A system with input x[n] and output y[n] is given as

The system is

(GATE 2006 || EC || PYQ || MCQ || 2 MARKS)

Linear, stable and invertible
non-linear, stable and non-invertible
Linear, stable and non-invertible
linear, unstable and invertible

Question 8

Let P be linearity, Q be time-invariance, R be causality and S be stability. A discrete-time system has the input-output relationship

where x(n) is the input and y(n) is the output. The above system has the properties

(GATE 2003 || EC || PYQ || MCQ || 2 MARKS)

P, S but not Q, R.
P, Q, S but not R.
P, Q, R, S.
Q, R, S but not P.

Question 9

A system with an input x(t) and output y(t) is described by the relation: y(t)=tx(t). This system is

(GATE 2000 || EC || PYQ || MCQ || 1 MARKS)

linear and time-invariant
linear and time varying
non-linear and time-invariant
non-linear and time-varying

Question 10

(GATE 2001 || EC || PYQ || MCQ || 1 MARKS)

1
-1
0
0

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