Z Transform Properties-1 MCQ’s

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

1. 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
View Answer

2. 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)

3. 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

4. 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

5. 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

6. 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

7. 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

9. 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

10. 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

11. 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)

12. 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

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