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# GATE EC 2021: Subject Revision Quiz 5 (App update required to attempt this test)

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Question 1

If a periodic signal has the Fourier coefficient X(k), and when the signal is delayed by 2sec its 5th harmonic gets delayed in phase by 0.1 radian, the fundamental frequency of the signal in milli rad/sec is ____

Question 2

X[z] of a system is specified by a pole zero pattern in below. Consider the three different solution of x[n]  Correct solution is

Question 3

The bilateral Laplace transform of u (- t + 5) is

Question 4

The magnitude and phase function’s for a Distortionless filter should respectively be Question 5

The maximum amplitude of cross correlated sequence of x(n)=(2,5,0,4) and h(n)=(3,1,4) is

Question 6

Consider a system with Input x(t) and Output y(t) related as follows:- Which one of the following statement about system is true?

Question 7

The periodic signal f(t) with period 2π and defined for one period as, f(t) = t – t2 from t = –π to t = π

Then find the value of Question 8

The response of a system to a unit impulse input is given by which of the following statement is correct about the system
(1) System is a linear system
(2) Steady state gain of the system for unit step input is 0.11
(3) Close loop system with unity feedback is stable

Question 9

Consider a system with impulse response given as . Find the eigen value of the system associated with the eigen function given as .

Question 10

Let be a periodic signal period 16. Its DFS coefficients are defined by for all k. The value of the coefficient a31 is____________.

Question 11

For the waveform shown in figure below  If Question 12

The bilateral Laplace transform of X(s) = d2/ds2 {(1/s -4)}  ROC: Re(s) > 4 The signal x(t) is

Question 13

The DTFT of a sequence x is X ( ).
Then find the value of   X ( )

Question 14

X[k] is the 6-point DFT of x[n]={3,2,1,0,0,3} and where Y[k] is the 6-point DFT of y[n] and . Then y[n] ?

Question 15

Consider the signal given below, If then the z-transform X(z) is
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