# Properties of Z-Transforms – 1 MCQ’s

This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Properties of Z-Transforms – 1″.

1. The z-transform of δ[n+k]>0 is __________
a) Z-k, Z≠0
b) Zk, Z≠0
c) Z-k, all Z
d) Zk, all Z

2. The z-transform of u[n] is _________
a) \frac{1}{1-z^{-1}}, |Z|>1
b) \frac{1}{1-z^{-1}}, |Z|<1
c) \frac{z}{1-z^{-1}}, |Z|<1
d) \frac{z}{1-z^{-1}}, |Z|>1

3. The z-transform of δ[n-k]>0 is __________
a) Zk, Z>0
b) Z-k, Z>0
c) Zk, Z≠0
d) Z-k, Z≠0

4. The z-transform of (\frac{1}{4})^n (u[n] – u[n-5]) is __________
a) \frac{z^5 – 0.25^5}{z^4 (z-0.25)}, z>0.25
b) \frac{z^5 – 0.25^5}{z^4 (z-0.25)}, z>0
c) \frac{z^5 – 0.25^5}{z^3 (z-0.25)}, z<0.25
d) \frac{z^5 – 0.25^5}{z^4 (z-0.25)}, all z

5. The z-transform of 3n u[-n-1] is ___________
a) \frac{z}{3-z}, |Z|>3
b) \frac{z}{3-z}, |Z|<3
c) \frac{3}{3-z}, |Z|>3
d) \frac{3}{3-z}, |Z|<3

6. The z-transform of cos(\frac{π}{3} n) u[n] is __________
a) \frac{z}{2} \frac{(2z-1)}{(z^2-z+1)}, 0<|z|<1
b) \frac{z}{2} \frac{(2z-1)}{(z^2-z+1)}, |z|>1
c) \frac{z}{2} \frac{(1-2z)}{(z^2-z+1)}, 0<|z|<1
d) \frac{z}{2} \frac{(1-2z)}{(z^2-z+1)}, |z|>1

7. The z-transform of (\frac{1}{4})^4 u[-n] is ___________
a) \frac{4z}{4z-1}, |Z|>\frac{1}{4}
b) \frac{4z}{4z-1}, |Z|<\frac{1}{4}
c) \frac{1}{1-4z}, |Z|>\frac{1}{4}
d) \frac{1}{1-4z}, |Z|<\frac{1}{4}

8. The z-transform of (\frac{2}{3})^{[n]} is ____________
a) \frac{-5z}{(2z-3)(3z-2)}, –\frac{3}{2} < z < –\frac{2}{3}
b) \frac{-5z}{(2z-3)(3z-2)}, \frac{2}{3} < |z| < \frac{3}{2}
c) \frac{5z}{(2z-3)(3z-2)}, \frac{2}{3} < |z|
d) \frac{5z}{(2z-3)(3z-2)}, –\frac{3}{2} < z< –\frac{2}{3}

9. The z-transform of {3,0,0,0,0,6,1,-4} (1 as the reference variable) is ___________
a) 3z5 + 6 + z-1 – 4z-2, 0≤|z|<∞
b) 3z5 + 6 + z-1 – 4z-2, 0<|z|<∞
c) 3z5 + 6 + z – 4z-2 0<|z|<∞
d) 3z5 + 6 + z-1 – 4z-2, 0≤|z|<∞

10. The z-transform of x[n]= {1,0,-1,0,1,-1} (1st 1 as the reference variable) is __________
a) 1+2z-2 -4 z-4 + 5z-5
b) 1-z-2 + z-4 – z-5
c) 1-2z2 + 4z4 – 5z5
d) 1-z2 + z4 – z5

11. Given the z-transform pair
X[n] \leftrightarrow \frac{32}{z^2-16}, |z|<4
The z-transform of the signal y[n] = \frac{1}{2^n} x[n] is _________
a) \frac{(z+2)^2}{(z+2)^2-16}
b) \frac{z^2}{z^2-4}
c) \frac{(z-2)^2}{(z-2)^2-16}
d) \frac{z^2}{z^2-64}

12. The z-transform of x[n]= {2,4,5,7,0,1} (5 as the reference variable) is ___________
a) 2z2 + 4z + 5 +7z + z3, z≠∞
b) 2z-2 + 4z-1 + 5 + 7z + z3, z≠∞
c) 2z-2 + 4z-1 + 5 + 7z + z3, 0<|z|<∞
d) 2z2 + 4z + 5 + 7z-1 + z3, 0<|z|<∞

13. Given the z-transform pair
X[n] \leftrightarrow \frac{32}{z^2-16}, |z|<4
The z-transform of the signal x [n-2] is _________
a) \frac{z^4}{z^2-16}
b) \frac{(z+2)^2}{(z+2)^2-16}
c) \frac{1}{z^2-16}
d) \frac{(z-2)^2}{(z-2)^2-16}

14. Given the z-transform pair
X[n] \leftrightarrow \frac{32}{z^2-16}, |z|<4
The z-transform of the signal x [-n]*x[n] is ____________
a) \frac{z^2}{16z^2-257z^4-16}
b) \frac{-16z^2}{(z^2-16)^2}
c) \frac{z^2}{(257z^2-16z^4-16)}
d) \frac{16z^2}{(z^2-16)^2}

15. Given the z-transform pair
X[n] \leftrightarrow \frac{32}{z^2-16}, |z|<4
The z-transform of the signal x[n]*x [n-3] is __________
a) \frac{z^{-3}}{(z^2-16)^2}
b) \frac{z^7}{(z^2-16)^2}
c) \frac{z^5}{(z^2-16)^2}
d) \frac{z}{(z^2-16)^2}

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