GATE EE topic:signals-and-systems PYQs & Answers — Page 5

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Questions 41–50 of 59. Imported answers require independent review unless marked reviewed.

Topic practice 59 questionsPage 5 of 6

Which of the following options is true for a linear time-invariant discrete time system that obeys the difference equation:

Your answerChoose one option.

is unaffected by the values of

The system is necessarily causal.

The system impulse response is non-zero at infinitely many instants.

When

, the function

is solely determined by the function

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The inverse Laplace transform of

for

Your answerChoose one option.

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The symbols,

and

, represent positive quantities, and

is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system?

Your answerChoose one option.

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A periodic function

, with a period of

, is represented as its Fourier series,

the Fourier series coefficients

and

are

Your answerChoose one option.

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A continuous-time input signal x(t) is an eigenfunction of an LTI system, if the output is

Your answerChoose one option.

k x(t), where k is an eigenvalue

, where k is an eigenvalue and

is a complex exponential signal

, where

is a complex exponential signal

k H(ω), where k is an eigenvalue and H(ω) is a frequency response of the system

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Consider the two continuous-time signals defined below:

These signals are sampled with a sampling period of

seconds to obtain discrete-time signals

and

, respectively. Which one of the following statements is true?

Your answerChoose one option.

The energy of

is greater than the energy of

The energy of

is greater than the energy of

and

have equal energies.

Neither

nor

is a finite-energy signal.

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The signal energy of the continuous-time signal

Your answerChoose one option.

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The Fourier transform of a continuous-time signal

is given by

, where

and

denotes frequency. Then the value of

is ________ (up to 1 decimal place). (ln denotes the logarithm to base e)

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Let

, where “

” denotes convolution. Let

be a positive real-valued constant. Choose the correct expression for

Your answerChoose one option.

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The pole-zero plots of three discrete-time systems P, Q and R on the z-plane are shown below.

Diagram for Electrical Engineering question 4

Which one of the following is TRUE about the frequency selectivity of these systems?

Your answerChoose one option.

All three are high-pass filters.

All three are band-pass filters.

All three are low-pass filters.

P is a low-pass filter, Q is a band-pass filter and R is a high-pass filter.

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GATE EE topic:signals-and-systems PYQs

Question 39

Question 1

Question 7

Question 28

Question 16

Question 38

Question 39

Question 40

Question 3

Question 4