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Test: Z Transform Properties - 2


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10 Questions MCQ Test Digital Signal Processing | Test: Z Transform Properties - 2

Test: Z Transform Properties - 2 for Electrical Engineering (EE) 2022 is part of Digital Signal Processing preparation. The Test: Z Transform Properties - 2 questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Z Transform Properties - 2 MCQs are made for Electrical Engineering (EE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Z Transform Properties - 2 below.
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Test: Z Transform Properties - 2 - Question 1

Sampling rate conversion by the rational factor I/D is accomplished by what connection of interpolator and decimator?

Detailed Solution for Test: Z Transform Properties - 2 - Question 1

Explanation: A sampling rate conversion by the rational factor I/D is accomplished by cascading an interpolator with a decimator.

Test: Z Transform Properties - 2 - Question 2

Which of the following has to be performed in sampling rate conversion by rational factor?

Detailed Solution for Test: Z Transform Properties - 2 - Question 2

Explanation: We emphasize that the importance of performing the interpolation first and decimation second, is to preserve the desired spectral characteristics of x(n).

Test: Z Transform Properties - 2 - Question 3

Which of the following operation is performed by the blocks given the figure below?

Detailed Solution for Test: Z Transform Properties - 2 - Question 3

Explanation: In the diagram given, a interpolator is in cascade with a decimator which together performs the action of sampling rate conversion by a factor I/D.

Test: Z Transform Properties - 2 - Question 4

 The Nth root of unity WN is given as: 

Detailed Solution for Test: Z Transform Properties - 2 - Question 4

Explanation: We know that the Discrete Fourier transform of a signal x(n) is given as

Thus we get Nth rot of unity WN= e-j2π/N

Test: Z Transform Properties - 2 - Question 5

Which of the following is true regarding the number of computations requires to compute an N-point DFT? 

Detailed Solution for Test: Z Transform Properties - 2 - Question 5

Explanation: The formula for calculating N point DFT is given as

From the formula given at every step of computing we are performing N complex multiplications and N-1 complex additions. So, in a total to perform N-point DFT we perform N2 complex multiplications and N(N-1) complex additions.

Test: Z Transform Properties - 2 - Question 6

Which of the following is true?

Detailed Solution for Test: Z Transform Properties - 2 - Question 6

Explanation: If XN represents the N point DFT of the sequence xN in the matrix form, then we know that

Test: Z Transform Properties - 2 - Question 7

What is the DFT of the four point sequence x(n)={0,1,2,3}?

Detailed Solution for Test: Z Transform Properties - 2 - Question 7

 

Explanation: The first step is to determine the matrix W4. By exploiting the periodicity property of W4 and the symmetry property


Test: Z Transform Properties - 2 - Question 8

 If X(k) is the N point DFT of a sequence whose Fourier series coefficients is given by ck, then which of the following is true? 

Detailed Solution for Test: Z Transform Properties - 2 - Question 8

Explanation: The Fourier series coefficients are given by the expression

Test: Z Transform Properties - 2 - Question 9

What is the DFT of the four point sequence x(n)={0,1,2,3}?

Detailed Solution for Test: Z Transform Properties - 2 - Question 9

Answer: Given x(n)={0,1,2,3}
We know that the 4-point DFT of the above given sequence is given by the expression

In this case N=4
=>X(0)=6,X(1)=-2+2j,X(2)=-2,X(3)=-2-2j.

Test: Z Transform Properties - 2 - Question 10

 If W4100=Wx200, then what is the value of x?

Detailed Solution for Test: Z Transform Properties - 2 - Question 10

Explanation: We know that according to the periodicity and symmetry property,
100/4=200/x=>x=8.

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