GATE ECE 2023 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2023

MCQ (Single Correct Answer)

-0.33

Let $$m(t)$$ be a strictly band-limited signal with bandwidth B and energy E. Assuming $${\omega _0} = 10B$$, the energy in the signal $$m(t)\cos {\omega _0}t$$ is

$${E \over 4}$$

$${E \over 2}$$

GATE ECE 2023

MCQ (Single Correct Answer)

-0.33

The Fourier transform $$x(\omega )$$ of $$x(t) = {e^{ - {t^2}}}$$ is

Note : $$\int\limits_{ - \infty }^\infty {{e^{ - {y^2}}}dy = \sqrt \pi } $$

$$\sqrt \pi {e^{{{{\omega ^2}} \over 2}}}$$

$${{{e^{ - {{{\omega ^2}} \over 4}}}} \over {2\sqrt \pi }}$$

$$\sqrt \pi {e^{ - {{{\omega ^2}} \over 4}}}$$

$$\sqrt \pi {e^{ - {{{\omega ^2}} \over 2}}}$$

GATE ECE 2023

MCQ (Single Correct Answer)

-0.33

In the table shown below, match the signal type with its spectral characteristics.

	Signal type		Spectral characteristics
(i)	Continuous, aperiodic	(a)	Continuous, aperiodic
(ii)	Continuous, periodic	(b)	Continuous, periodic
(iii)	Discrete, aperiodic	(c)	Discrete, aperiodic
(iv)	Discrete, periodic	(d)	Discrete, periodic

$$(i)\to(a),(ii)\to(b),(iii)\to(c),(iv)\to(d)$$

$$(i)\to(a),(ii)\to(c),(iii)\to(b),(iv)\to(d)$$

$$(i)\to(d),(ii)\to(b),(iii)\to(c),(iv)\to(a)$$

$$(i)\to(a),(ii)\to(c),(iii)\to(d),(iv)\to(b)$$

GATE ECE 2023

MCQ (Single Correct Answer)

-0.67

Consider a discrete-time periodic signal with period N = 5. Let the discrete-time Fourier series (DTFS) representation be $$x[n] = \sum\limits_{k = 0}^4 {{a_k}{e^{{{jk2\pi m} \over 5}}}} $$, where $${a_0} = 1,{a_1} = 3j,{a_2} = 2j,{a_3} = - 2j$$ and $${a_4} = - 3j$$. The value of the sum $$\sum\limits_{n = 0}^4 {x[n]\sin {{4\pi n} \over 5}} $$ is

$$-$$10

$$-$$2

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