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# GATE EC 2021: National Champion Quiz 4 (App update required to attempt this test)

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Question 1

Which country has been elected to the UNICEF Executive Board, representing the group of Asia-Pacific countries for the term 2016-2018?

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

The Hilbert transform of x(t)=ej2πft 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 the following statements regarding a linear system y= f(x1)
1) f(x1+x2)=f(x1) + f(x2)
2) f[x(t+T)]= f[x(t)]+f[x(T)]
3) f(Kx)=Kf(x)
Of these statements

Question 8

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

Question 9

Given that periodic signal (t) has Fourier coefficient X(k) and fundamental frequency .
T
he Fourier coefficient of (t) = (-2t + 4), with fundamental frequency  is

Question 10

The z-transfrom of a system is
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

Two systems S1 and S2 are cascaded where

S1 : P(n) = 3P(n – 1) + x(n)

S2 : y(n) = k1y(n – 1) + k2P(n)

If the overall input output relation is given by y(n) + 3 y (n – 2) – 4y(n – 2) = 4x (n) then value of K1 + K2 is ……

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