Z Transform Properties

Digital Communications Systems

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Properties of Z Transform-1”.

1. Which of the following justifies the linearity property of z-transform?[x(n)↔X(z)].
a) x(n)+y(n) ↔ X(z)Y(z)
b) x(n)+y(n) ↔ X(z)+Y(z)
c) x(n)y(n) ↔ X(z)+Y(z)
d) x(n)y(n) ↔ X(z)Y(z)

2. What is the z-transform of the signal x(n)=[3(2n)-4(3n)]u(n)?
a) 31−2z−1−41−3z−1
b) 31−2z−1−41+3z−1
c) 31−2z−41−3z
d) None of the mentioned

3. What is the z-transform of the signal x(n)=sin(jω0n)u(n)?
a) z−1sinω01+2z−1cosω0+z−2
b) z−1sinω01−2z−1cosω0−z−2
c) z−1cosω01−2z−1cosω0+z−2
d) z−1sinω01−2z−1cosω0+z−2

4. According to Time shifting property of z-transform, if X(z) is the z-transform of x(n) then what is the z-transform of x(n-k)?
a) zkX(z)
b) z-kX(z)
c) X(z-k)
d) X(z+k)

5. What is the z-transform of the signal defined as x(n)=u(n)-u(n-N)?
a) 1+zN1+z−1
b) 1−zN1+z−1
c) 1+z−N1+z−1
d) 1−z−N1−z−1

6. If X(z) is the z-transform of the signal x(n) then what is the z-transform of anx(n)?
a) X(az)
b) X(az-1)
c) X(a-1z)
d) None of the mentioned

7. If the ROC of X(z) is r1<|z|<r2, then what is the ROC of X(a-1z)?
a) |a|r1<|z|<|a|r2
b) |a|r1>|z|>|a|r2
c) |a|r1<|z|>|a|r2
d) |a|r1>|z|<|a|r2

8. What is the z-transform of the signal x(n)=an(sinω0n)u(n)?
a)az−1sinω01+2az−1cosω0+a2z−2
b)az−1sinω01−2az−1cosω0−a2z−2
c)(az)−1cosω01−2az−1cosω0+a2z−2
d)az−1sinω01−2az−1cosω0+a2z−2

9. If X(z) is the z-transform of the signal x(n), then what is the z-transform of the signal x(-n)?
a) X(-z)
b) X(z-1)
c) X-1(z)
d) None of the mentioned

10. X(z) is the z-transform of the signal x(n), then what is the z-transform of the signal nx(n)?
a) −zdX(z)dz
b) zdX(z)dz
c) −z−1dX(z)dz
d) z−1dX(z)dz

11. What is the z-transform of the signal x(n)=nanu(n)?
a) (az)−1(1−(az)−1)2
b) az−1(1−(az)−1)2
c) az−1(1−az−1)2
d) az−1(1+az−1)2

12. Sampling rate conversion by the rational factor I/D is accomplished by what connection of interpolator and decimator?
a) Parallel
b) Cascade
c) Convolution
d) None of the mentioned

13. Which of the following has to be performed in sampling rate conversion by rational factor?
a) Interpolation
b) Decimation
c) Either interpolation or decimation
d) None of the mentioned

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

a) Sampling rate conversion by a factor I
b) Sampling rate conversion by a factor D
c) Sampling rate conversion by a factor D/I
d) Sampling rate conversion by a factor I/D

15. The Nth root of unity WN is given as _____________
a) ej2πN
b) e-j2πN
c) e-j2π/N
d) ej2π/N

16. Which of the following is true regarding the number of computations requires to compute an N-point DFT?
a) N2 complex multiplications and N(N-1) complex additions
b) N2 complex additions and N(N-1) complex multiplications
c) N2 complex multiplications and N(N+1) complex additions
d) N2 complex additions and N(N+1) complex multiplications

17. Which of the following is true?
a) W∗N=1NWN−1
b) WN−1=1NWN∗
c) WN−1=WN∗
d) None of the mentioned

18. 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?
a) X(k)=Nck
b) X(k)=ck/N
c) X(k)=N/ck
d) None of the mentioned

19. What is the DFT of the four point sequence x(n)={0,1,2,3}?
a) {6,-2+2j-2,-2-2j}
b) {6,-2-2j,2,-2+2j}
c) {6,-2-2j,-2,-2+2j}
d) {6,-2+2j,-2,-2-2j}

20. If W4100=Wx200, then what is the value of x?
a) 2
b) 4
c) 8
d) 16

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