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

## 15 Questions MCQ Test GATE ECE (Electronics) 2023 Mock Test Series | Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform

Description
Attempt Test: The Continuous, Time Fourier Series & The Discrete, Time Fourier Transform | 15 questions in 45 minutes | Mock test for Electronics and Communication Engineering (ECE) preparation | Free important questions MCQ to study GATE ECE (Electronics) 2023 Mock Test Series for Electronics and Communication Engineering (ECE) Exam | Download free PDF with solutions
QUESTION: 1

### Determine the Fourier series coefficient for given periodic signal x(t). Que: x(t) as shown in fig.   ​

Solution:

A = 10 , T = 5, X [k] = 2

QUESTION: 2

Solution:

QUESTION: 3

### Determine the Fourier series coefficient for given periodic signal x(t). Que: x(t) as shown in fig. ​ ​ ​

Solution:

QUESTION: 4

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

Que: x(t) as shown in fig.

​ ​ ​

Solution:

QUESTION: 5

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

x(t) = sin2t

Solution:

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.

Solution:

= 2(cos 6πt - sin 2πt)

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.

Solution:

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

Solution:

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

Solution:

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

Solution:

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 )

Solution:

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

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)}

Solution:

The FS coefficients of x(t) are

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

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)}

Solution:

QUESTION: 14

Determine the signal having the Fourier transform given in question.

Solution:

QUESTION: 15

Determine the signal having the Fourier transform given in question.

Solution:

 Use Code STAYHOME200 and get INR 200 additional OFF Use Coupon Code

### Download free EduRev App

Track your progress, build streaks, highlight & save important lessons and more!