# Test: Signals & Systems - 1

## 15 Questions MCQ Test GATE ECE (Electronics) 2023 Mock Test Series | Test: Signals & Systems - 1

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Attempt Test: Signals & Systems - 1 | 15 questions in 45 minutes | Mock test for Electronics and Communication Engineering (ECE) preparation | Free important questions MCQ to study GATE ECE (Electronics) 2023 Mock Test Series for Electronics and Communication Engineering (ECE) Exam | Download free PDF with solutions
QUESTION: 1

### If a real function f(t) has Fourier transform F(ω), then Fourier transform of f(t) - f(-t) will be

Solution:  If F(w)is a complex no.a+jb

then Ft (w) is (a-jb)

SoF.T.of f(t)-f(-t) will bean imaginary number equal to (2 jb)

QUESTION: 2

### If impulse response of a discrete time LTI system is an u[n] then its step response is

Solution:  QUESTION: 3

### Q. If transfer function H(s) of a system is given as H(s) = < Re {s} < -1 then value of h(t) is given as.

Solution:

Take partial fraction and then take inverse according to range of ROC.

QUESTION: 4

if u(t) is unit step and δ(t) is unit impulse function then Inverse z, Transform of F(z) = 1/z + 1For k > 0 is

Solution:
QUESTION: 5

What is the value of Fundamental period of sequence x[n] = 3 sin (1.3 nπ+ π/2) + sin (1.2π)

Solution:
QUESTION: 6

If Fourier transform of x[n] is X(e'°') then Fourier transform of (- 1)n x[n] will be

Solution:  QUESTION: 7

A continuous time system is described by where y(t) is output and x(t) is input, then y(t)is bounded.

Solution: if x (t) is not bounded then is bounded.

QUESTION: 8

Magnitude of Fourier transform x(t) & y(t) are shown in figure. If phases of X(ω) and Y(ω) are zero for all w. The magnitude and frequency units are identical in both figure then relation between y(t) and x(t) is expressed as :  Solution:
QUESTION: 9

X (z) = , if lal & Ibl < 1 with ROC, specified as

|a| < |z| < |b| then x  of corresponding sequence is given by.

Solution: QUESTION: 10

If impulse response of a system is h(t) = e-|t|then.

Solution: so it is a non - causal system. So         it is a stable - system.

QUESTION: 11

A box has 4 white and 3 red balls. Two balls are taken out in succession. What is the probability that both are white?

Solution:
QUESTION: 12

For a given discrete time sequencex[n] = 2, 0, - 1, - 3, 4, 1, - 1 ) then value of X (e) is

Solution:
QUESTION: 13

Which of the following transfer function corresponds to an unstable system

Solution:
QUESTION: 14

14 If average power and energy of signal u(t) are P and E then

Solution:

Just use formula for energy and power.

QUESTION: 15

The value of δ(at) and δ(an) are respectively.

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