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GATE EC : Signals & Systems Champion Quiz 1

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Question 1

The Fourier series expansion of a real periodic signal with fundamental frequency f_o is given by it is given that C₃ = 3+j 5 Then C_-3 is

Question 2

Let and h(t) is a filter matched to g(t) is applied as input to h(t), then the Fourier transform of the output is

Question 3

The Fourier transform of a signal x(t) = e^–4|t| is

Question 4

The Fourier transform of a conjugate symmetric function is always

Question 5

The magnitude and phase of the complex Fourier series coefficients a_k of a periodic signal x(t) are shown in the figure. Choose the correct statement from the four choices given. Notation: C is the set of complex numbers, R is the set of purely real numbers, and P is the set of purely imaginary numbers.
$Description: Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-2_files\image084.png$

Question 6

Given

. If

, then the value of K is

Question 7

The Fourier transform of a signal h(t) is H(jω) = (2cosω)(sin2ω)/ω. The value of h(0) is

Question 8

For a signal x(t) the Fourier transform is X(f). Then the inverse Fourier transform of X(3f + 2) is given by

Question 9

The signal x(t) is described by

Two of the angular frequencies at which its Fourier transform becomes zero are

Question 10

Let $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-3_files\image191.png$ be a periodic signal period 16. Its DFS coefficients are defined by $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-3_files\image192.png$ for all k. The value of the coefficient a₃₁ is____________.

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ESE & GATE EC Signals and Systems

Apr 24ESE & GATE EC