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GATE EC 2022: National Champion Quiz signal & system

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Question 1

Consider a energy signal x(t) having energy ‘E’, if x(t) and x(-t) are orthogonal to each other then energy of its even symmetric part will be equal to

Question 2

Consider two real valued signals, x(t) band-limited to [−500 Hz, 500Hz] and y(t) band-limited to [−1kHz, 1kHz]. For z (t) = x(t). y(t), the Nyquist sampling frequency (in kHz) is __________

Question 3

Hilbert transform of is

Question 4

The 4-point DFT of the sequence x(n)=cos(nπ/4) is X(k).

Then find the value of

Question 5

For the pole –zero plot shown in figure represents ________filter

Question 6

Consider a periodic signal with time period T=2. The derivative of this signal is related to the impulse train with period T=2. It can be shown that
then the value of and are

Question 7

Consider a unit delay element:

Determine whether the system is memoryless, causal and linear

Question 8

The exponential Fourier series coefficient of the periodic signal shown in the figure will be

Question 9

Consider a periodic signal x(t) whose Fourier series coefficient is defined as below

Which of the following is true?

Question 10

The z-transfrom of a system is Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC-ME-17-Mar\GATE-ECE-2004_files\image058.png
If the ROC is |z| < 0.2, then the impulse response of the system is

Question 11

A signal is represented as x (t) whose Laplace transform is denoted by X (s) where The value of signal x (t) at t = 1 sec is __________.

Question 12

Consider a cascaded system

S1: w[n] = 2w [n – 1] + x[n]

S2: y[n] = k1y[n – 1] +k2w[n]

Cascaded: y[n] + 6 y [n – 2] –5y [n – 1] = 2x(n)

the value of k1/k2is____

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Dec 22ESE & GATE EC