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Test: The Discrete -Time Fourier Series - Electrical Engineering (EE) MCQ


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15 Questions MCQ Test GATE Electrical Engineering (EE) Mock Test Series 2025 - Test: The Discrete -Time Fourier Series

Test: The Discrete -Time Fourier Series for Electrical Engineering (EE) 2024 is part of GATE Electrical Engineering (EE) Mock Test Series 2025 preparation. The Test: The Discrete -Time Fourier Series questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: The Discrete -Time Fourier Series MCQs are made for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: The Discrete -Time Fourier Series below.
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Test: The Discrete -Time Fourier Series - Question 1

Consider a periodic signal x[n] with period N and FS coefficients X [k]. Determine the FS coefficients Y [k] of the signal y[n] given in question.

Que: y[n] = x[ n - no]

Detailed Solution for Test: The Discrete -Time Fourier Series - Question 1

Test: The Discrete -Time Fourier Series - Question 2

Consider a periodic signal x[n] with period N and FS coefficients X [k]. Determine the FS coefficients Y [k] of the signal y[n] given in question.

y[n] = x[n] - x[n-2 ]

Detailed Solution for Test: The Discrete -Time Fourier Series - Question 2

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Test: The Discrete -Time Fourier Series - Question 3

Consider a periodic signal x[n] with period N and FS coefficients X [k]. Determine the FS coefficients Y [k] of the signal y[n] given in question.

Que: y[n] =  x[n] + x[n + N/2 ] , (assume that N is even)

Detailed Solution for Test: The Discrete -Time Fourier Series - Question 3

Note that y[n] =  x[n] + x[n + N/2 ] has a period of N/2 and N has been assumed to be even,

Test: The Discrete -Time Fourier Series - Question 4

Consider a periodic signal x[n] with period N and FS coefficients X [k]. Determine the FS coefficients Y [k] of the signal y[n] given in question.

Que: y[n] = x[n] - x[n + N/2 ] , (assume that N is even)

Detailed Solution for Test: The Discrete -Time Fourier Series - Question 4

Test: The Discrete -Time Fourier Series - Question 5

Consider a periodic signal x[n] with period N and FS coefficients X [k]. Determine the FS coefficients Y [k] of the signal y[n] given in question.

Que: y[n] = x*[-n]

Detailed Solution for Test: The Discrete -Time Fourier Series - Question 5

y[n] = x*[-n]

Test: The Discrete -Time Fourier Series - Question 6

Consider a periodic signal x[n] with period N and FS coefficients X [k]. Determine the FS coefficients Y [k] of the signal y[n] given in question.

y[n] = (-1)nx[n], (assume that N is even)

Detailed Solution for Test: The Discrete -Time Fourier Series - Question 6

With N even

Test: The Discrete -Time Fourier Series - Question 7

Consider a discrete-time periodic signal

with period  N = 10, Also y[n] = x[n] - x[n-1]

Que: The FS coefficients of y[n] are

Detailed Solution for Test: The Discrete -Time Fourier Series - Question 7

Test: The Discrete -Time Fourier Series - Question 8

Consider a discrete-time signal with Fourier representation.

In question the FS coefficient Y [k] is given. Determine the corresponding signal y[n] and choose correct option.

Que: Y[k] = X[k-5] + X[k+5]

Detailed Solution for Test: The Discrete -Time Fourier Series - Question 8

Test: The Discrete -Time Fourier Series - Question 9

onsider a discrete-time signal with Fourier representation.

In question the FS coefficient Y [k] is given. Determine the corresponding signal y[n] and choose correct option.

Que: 

Detailed Solution for Test: The Discrete -Time Fourier Series - Question 9

Test: The Discrete -Time Fourier Series - Question 10

Consider a discrete-time signal with Fourier representation.

In question the FS coefficient Y [k] is given. Determine the corresponding signal y[n] and choose correct option.

Que: Y[k] = X[k]*X[k]

Detailed Solution for Test: The Discrete -Time Fourier Series - Question 10

Test: The Discrete -Time Fourier Series - Question 11

Consider a discrete-time signal with Fourier representation.

In question the FS coefficient Y [k] is given. Determine the corresponding signal y[n] and choose correct option.

Que: Y[k] = Re{X[k]}

Detailed Solution for Test: The Discrete -Time Fourier Series - Question 11

Test: The Discrete -Time Fourier Series - Question 12

Consider a signal x[n] with following facts

1. x[n] is a real and even signal

2. The period of x[n] is N = 10

3. X [11] = 5​ ​ ​ ​

 

Detailed Solution for Test: The Discrete -Time Fourier Series - Question 12

Since N = 10, X[11] = X[1] = 5
Since x[n] is real and even X[k] is also real and even.
Therefore X[1] = X[-1] = 5.

Test: The Discrete -Time Fourier Series - Question 13

Let an input x[n] having discrete time Fourier transform  be passed through an LTI system. The frequency response of the LTI system is  The output y[n] of the system is

Detailed Solution for Test: The Discrete -Time Fourier Series - Question 13

Given: ��[��] = x[n] ∗ h[n]
We know that the convolution in one domain results in convolution in another domain.

Taking IDFT we have:

Test: The Discrete -Time Fourier Series - Question 14

Consider a signal defined by

Its Fourier Transform is

Detailed Solution for Test: The Discrete -Time Fourier Series - Question 14

Concept:
The Fourier Transform of a continuous-time signal x(t) is given as:

Analysis:

Given:

x(t) = ej10t  defined from t = -1 to 1. 

Test: The Discrete -Time Fourier Series - Question 15

The frequency response and the main lobe width for rectangular window are

Detailed Solution for Test: The Discrete -Time Fourier Series - Question 15

The rectangular window is the most common windowing technique to design a finite impulse response (FIR) filter.
A rectangular window is defined as

Where N = length of the FIR filter
The frequency response of wR(n) is wR(ω) which is calculated as:
wR(ω) = DTFT of wR(n), i.e.

ω ϵ [-π, π] rad/sec
For the given rectangular sequence, the Fourier transform will be a sinc sequence given by:

The spectrum is as shown:

Main-lobe width = 2 × (zero-crossing points of sin c function), i.e.

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