Electronics and Communication Engineering
GATE ECE topic:continuous-time-signals PYQs
Build your understanding with focused practice from past exam papers.
Questions 31–36 of 36. Imported answers require independent review unless marked reviewed.
Question 31
Open questionECMCQ2 marksNeeds review
Let
be a continuous time periodic signal with fundamental period
seconds. Let
be the complex Fourier series coefficients of
, where
is integer valued. Consider the following statements about
:I. The complex Fourier series coefficients of
are
where
is integer valued
II. The complex Fourier series coefficients of
are
where
is integer valued
III. The fundamental angular frequency of
is
rad/sFor the three statements above, which one of the following is correct?
Your answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 33
Open questionECNAT2 marksNeeds review
Consider an LTI system with magnitude response
and phase response
. If the input to the system is
then the average power of the output signal
is ________.Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 34
Open questionECNAT2 marksNeeds review
The transfer function of a causal LTI system is
. If the input to the system is
, where
is a unit step function, the system output
as
is ________.Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 35
Open questionECNAT2 marksNeeds review
Consider the parallel combination of two LTI systems shown in the figure. The impulse responses of the systems are
and
. If the input
is a unit step signal, then the energy of
is ________. 
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 49
Open questionECMCQ2 marksNeeds review
The signal
, where
is in seconds, is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal lowpass filter with frequency response
as follows:
What is the number of sinusoids in the output and their frequencies in kHz?
Your answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 52
Open questionECNAT2 marksNeeds review
A continuous time signal
, where
is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response
Let
be the output of this filter. The maximum value of
is ________.Log in to check the answer
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