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# GATE 2024 Signals & Systems Rank Booster Quiz 23

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Question 1

Consider a periodic signal x(t) described for one period as follows :

The trigonometric Fourier series representation of x(t) equals to

What is the value of coefficient a3?

Question 2

Consider a continuous time signal g(t) as

What is the energy for signal g(2t)?

Question 3

Consider a periodic signal x(t) described for one period as

What is the sum of power contained by first, second and third harmonic of the signal?

Question 4Multiple Correct Options

A system with input x(t) and output y(t) is described by y(t) = x[g(t)], where g(t) = cos t. Choose the correct statement.

Question 5

A discrete-time system with x(n) as input and output as y(n) is given by y(n) = (n – 3) x2(n – 3). Then the system having following statement:

1). System is non-linear.

2). System is time-varying.

3). System is stable.

4). system is not anticipatory.

Choose the correct statement.

Question 6

Let x(n) = then the value of is ____.

Question 7

A signal x(t) = e–2t u(t) is passed through an ideal low pass filter with cut-off frequency 1rad/sec. What is the output energy?
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