# Z Transform Properties-1 MCQ’s

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

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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)=a^{n}(sinω_{0}n)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)=na^{n}u(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(jω_{0}n)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 a^{n}x(n)?

a) X(az)

b) X(az^{-1})

c) X(a^{-1}z)

d) None of the mentioned

10. If the ROC of X(z) is r_{1}<|z|<r_{2}, then what is the ROC of X(a^{-1}z)?

a) |a|r_{1}<|z|<|a|r_{2}

b) |a|r_{1}>|z|>|a|r_{2}

c) |a|r_{1}<|z|>|a|r_{2}

d) |a|r_{1}>|z|<|a|r_{2}

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) z^{k}X(z)

b) z^{-k}X(z)

c) X(z-k)

d) X(z+k)

12. What is the z-transform of the signal x(n)=[3(2^{n})-4(3^{n})]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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