Free Printable Z Transforms

1.

Z transforms of unit step function is

a)

$\frac{\text{z}}{\text{z-a}}$

b)

$\frac{\text{z}}{\text{z-1}}$

c)

1

d)

0

2.

Which of the following is damping rule?

a)

$Z\left\{n\left(f\left(n\right)\right)\right\}=-z\frac{\text{d}}{\text{d}}F\left(\text{}z\right)$

b)

$Z\left\{f\left(n-k\right)\right\}=z^{-n}F\left(z\right)$

c)

$Z\left\{f\left(n+1\right)\right\}=zF\left(z\right)-zf\left(0\right)$

d)

$Z\left\{a^nf\left(n\right)\right\}=F\left(\frac{z}{a}\right)$

3.

$If\ Z\left\{f\left(n\right)\right\}=F\left(z\right)\ then\ f\left(0\right)=\lim_{z\rightarrow\infty}F\left(z\right)\ is\ called$

a)

$First\ shifting\ theorem$

b)

$Second\ shifting\ theorem$

c)

$Initial\ value\ theorem$

d)

$Final\ value\ theorem$

4.

The convolution theorem of Z- Transform is

a)

$Z^{-1}\left\{F\left(z\right)G\left(z\right)\right\}=f\left(n\right)\cdot g\left(n\right)$ $Z^{-1}\left\{F\left(z\right)G\left(z\right)\right\}=f\left(n\right)\cdot g\left(n\right)$

b)

$Z^{-1}\left\{F\left(z\right)+G\left(z\right)\right\}=f\left(n\right)+g\left(n\right)$

c)

$Z^{-1}\left\{F\left(z\right)-G\left(z\right)\right\}=f\left(n\right)-g\left(n\right)$

d)

$Z^{-1}\left\{\left(\frac{F\left(z\right)}{G\left(z\right)}\right)\right\}=\frac{f\left(n\right)}{g\left(n\right)}$

5.

What are the types used to solve inverse Z Transform

(a)

6.

$Z\left[\frac{1}{n}\right]=$

a)

$\log\left(\frac{1}{z-1}\right)$

b)

$\log\left(\frac{z}{z-1}\right)$

c)

$\log\ \left(\frac{1}{z+1}\right)$

d)

$\log\left(z-1\right)$

7.

$Z\left\{\delta\left(n-3\right)\right\}=$

a)

$\frac{1}{z}$ $\frac{1}{z}$

b)

$\frac{1}{z^2}$

c)

$\frac{1}{z^3}$

d)

$\frac{1}{z^k}$

8.

$Z\left\{\frac{1}{n!}\right\}=$

a)

$e^{-z}$

b)

$e^z$

c)

$e^{-\frac{1}{z}}$

d)

$e^{\frac{1}{z}}$

9.

$Z\left[k\right]=$

a)

$\frac{1}{z-1}$

b)

$\frac{z}{z+1}$

c)

$k\frac{z}{z-1}$

d)

$\frac{z}{z-1}$

10.

$Z\left\{nC_k\right\}=$

a)

$\left(1+z^{-1}\right)^n$

b)

$\left(1-z^{-1}\right)^n$

c)

$\left(1+z^{-1}\right)^k$

d)

$\left(1-z^{-1}\right)^k$

11.

$Z\left\{t\right\}=$

a)

$\frac{tz}{\left(z-1\right)^2}$

b)

$\frac{z}{\left(z-1\right)^2}$

c)

$\frac{z}{z-1}$

d)

$\frac{Tz}{\left(z-1\right)^2}$

12.

$Z\left\{\frac{a^n}{n!}\right\}$

a)

$e^{az}$

b)

$e^z$

c)

$e^{\frac{a}{z}}$

d)

$e^{\frac{1}{z}}$

13.

$Z\left\{a^n+5\right\}$

a)

$a^5\ \frac{z}{z-a}$

b)

$\frac{z}{z-a}$

c)

$a^2\ \frac{z}{z-1}$

d)

$\frac{z}{z-1}$

14.

$Z^{-1}\left\{\frac{z^2}{z^2+1}\right\}=$

a)

$\cos\ \frac{\pi}{4}$

b)

$\cos\ \frac{\pi}{2}$

c)

$\cos\ \frac{n\pi}{4}$

d)

$\cos\ \frac{\text{}n\pi}{\text{2}}$

15.

$Z^{-1}\left\{\frac{z}{z+3}\right\}=$

a)

$\left(3\right)^n$

b)

$\left(-3\right)^n$

c)

$\left(3\right)^{-n}$

d)

None of these

16.

$Z^{-1}\left\{\frac{1}{z-\frac{2}{5}}\right\}=$

a)

$a^n$

b)

$\left(\frac{2}{5}\right)^n$

c)

$\left(\frac{2}{5}\right)^{\left(n-1\right)}$

d)

$a^n-1$

17.

$Z^{-1}\left\{\frac{2z}{\left(z-2\right)^2}\right\}=$

a)

$\left(n+1\right)2^n$

b)

$n2^n$

c)

$2^n$

d)

$\left(n-1\right)2^n$

18.

Relation between difference operator and shifting operator

a)

$1+E+\Delta=0$

b)

$\Delta=1+E$

c)

$1=E+\Delta$

d)

$E=1+\Delta$

19.

$Z\left\{y_{\left(n+1\right)}\right\}=$

a)

$z\ \left\{\ \overline{y}\left(z\right)-y\left(0\right)\right\}$

b)

$\left\{\ \overline{y}\left(z\right)-y\left(0\right)\right\}$

c)

$z\ \left\{\ \overline{y}\left(z\right)+y\left(0\right)\right\}$

d)

$z\ \left\{\ \overline{y}\left(z\right)\right\}$

20.

$Find\ the\ simple\ pole\ or\ poles\ of\ F\left(z\right)=\frac{z}{\left(z-1\right)\left(z+2\right)}$

a)

1 and 2

b)

-1 and 2

c)

1 and -2

d)

-1 and -2

Z Transforms

Total questions: 20

Worksheet time: 11mins

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