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Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform


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15 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform

Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform for Electronics and Communication Engineering (ECE) 2022 is part of GATE Electrical Engineering (EE) 2023 Mock Test Series preparation. The Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform MCQs are made for Electronics and Communication Engineering (ECE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform below.
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Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 1

Determine the Fourier series coefficient for given periodic signal x(t).

Que: x(t) as shown in fig.

 

Detailed Solution for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 1

A = 10 , T = 5, X [k] = 2

Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 2

Determine the Fourier series coefficient for given periodic signal x(t).

Que: x(t) as shown in fig.

​ ​ ​

Detailed Solution for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 2

Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 3

Determine the Fourier series coefficient for given periodic signal x(t).

Que: x(t) as shown in fig.

​ ​ ​

Detailed Solution for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 3

Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 4

Determine the Fourier series coefficient for given periodic signal x(t).

Que: x(t) as shown in fig.

​ ​ ​

Detailed Solution for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 4

Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 5

Determine the Fourier series coefficient for given periodic signal x(t).

x(t) = sin2t

Detailed Solution for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 5

Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 6

In the question, the FS coefficient of time-domain signal have been given. Determine the corresponding time domain signal and choose correct option.

Detailed Solution for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 6

 = 2(cos 6πt - sin 2πt)

Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 7

In the question, the FS coefficient of time-domain signal have been given. Determine the corresponding time domain signal and choose correct option.

 

Detailed Solution for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 7

Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 8

In the question, the FS coefficient of time-domain signal have been given. Determine the corresponding time domain signal and choose correct option.

Que: X[k] as shown in fig, wo  = π 

 

Detailed Solution for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 8

Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 9

In the question, the FS coefficient of time-domain signal have been given. Determine the corresponding time domain signal and choose correct option.

Que: X[k] As shown in fig. , ωo = 2π

Detailed Solution for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 9

Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 10

In the question, the FS coefficient of time-domain signal have been given. Determine the corresponding time domain signal and choose correct option.

Que: X[k] As shown in fig. , ωo = π

Detailed Solution for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 10

Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 11

Consider a continuous time periodic signal x(t) with fundamental period T and Fourier series coefficients X[k]. Determine the Fourier series coefficient of the signal y(t) given in question and choose correct option.

Que: y(t) = x(t - t0 ) + x (t - t0 )

Detailed Solution for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 11

x(t - t0) is also periodic with T.  TheFourier series coefficients X1[k] of x(t - t0) are

Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 12

Consider a continuous time periodic signal x(t) with fundamental period T and Fourier series coefficients X[k]. Determine the Fourier series coefficient of the signal y(t) given in question and choose correct option.

Que: y(t) = Ev{x(t)}

Detailed Solution for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 12

The FS coefficients of x(t) are

Therefore, the FS coefficients of Ev{ x(t)} are

Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 13

Consider a continuous time periodic signal x(t) with fundamental period T and Fourier series coefficients X[k]. Determine the Fourier series coefficient of the signal y(t) given in question and choose correct option.

Que: y(t) = Re{x(t)}

Detailed Solution for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 13

Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 14

Determine the signal having the Fourier transform given in question.

Detailed Solution for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 14

Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 15

Determine the signal having the Fourier transform given in question.

Detailed Solution for Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform - Question 15

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