GATE ECE concept:fourier-series PYQs & Answers

Questions 1–6 of 6. Imported answers require independent review unless marked reviewed.

The continuous time signal

is real, periodic with period

and satisfies the Dirichlet conditions.

The Fourier series representation of

and

satisfies the following:

For any integer

, which of the following options is correct?

Your answerChoose one option.

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Let

be a periodic signal with fundamental period

. Consider the signal

, where

. The Fourier series expansions of

and

are given by

Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

for all

is periodic with a fundamental period

for all

is periodic with a fundamental period

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The exponential Fourier series representation of a continuous-time periodic signal

is defined as

where

is the fundamental angular frequency of

and the coefficients of the series are

. The following information is given about

and

is real and even, having a fundamental period of 6 II. The average value of

is 2 III.

The average power of the signal

(rounded off to one decimal place) is ________.

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Let

be a periodic function with period

. The Fourier series coefficients for this series are denoted by

, that is

The same function

can also be considered as a periodic function with period

. Let

be the Fourier series coefficients when period is taken as

. If

, then

is equal to

Your answerChoose one option.

256

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A periodic signal

has a trigonometric Fourier series expansion

, we can conclude that

Your answerChoose one option.

are zero for all

and

are zero for

even

are zero for all

and

are zero for

odd

are zero for

even and

are zero for

odd

are zero for

odd and

are zero for

even

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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

rad/s

For the three statements above, which one of the following is correct?

Your answerChoose one option.

only II and III are true

only I and III are true

only III is true

only I is true

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GATE ECE concept:fourier-series PYQs

How to practice concept:fourier-series

Question 37

Question 55

Question 39

Question 14

Question 8

Question 31