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GATE 2023 Signal & System Evaluation Quiz 6

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Question 1

A system described by the following differential equation is

Question 2

Consider two signals x(t) and y(t) shown in figure and their Laplace transform pairs and

If , then Y(s) will be

Question 3

Consider the function x(t) = u

The graph of x(t) is

Question 4

A system has the following output relationship

the impulse response of the system is

δ(t) - e–at u(t) such that the value of a is __________.

Question 5

Let x(t) be a signal whose Fourier transform is shown in figure

Then the magnitude spectrum of y(t) = t x(t)

Question 6

The transfer function of an FIR filter is given by

An analog signal is applied to this filter after sampling at a rate of 18 kHz. Which one of the following analog frequencies is not allowed by the filter?

Question 7

The discrete time Fourier Transform of a signal is given by

The value of , and are respectively given by:

Question 8

The Fourier transform of the function,  is obtained:

Determine the Fourier transform of the given function x(t).  Where 
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