Free Printable SS- Revision 3

1.

Which of the following is a causal system?

a)

$y\left(t\right)=x\left(t^2\right)$

b)

$y\left(t\right)=x^2\left(t\right)$

c)

$y\left(t\right)=x\left(-t\right)$

d)

$y\left(t\right)=x\left(2t\right)$

2.

Find the Fourier series representation of the signal is

x\left(t\right)=\frac{\cos2\pi t}{3}

and determine the Fourier series coefficients.

a)

$c_0=1,\ c_1=\frac{1}{6},\ c_{-1}=\frac{1}{6}$

b)

$c_1=\frac{1}{6}$

c)

$c_{-1}=\frac{1}{6}$

d)

$c_1=\frac{1}{6},\ c_{-1}=\frac{1}{6}$

3.

If a periodic signal has an even symmetry, then Fourier series contains

a)

Only sine terms

b)

Only cosine terms

c)

Constant and cosine terms

d)

Both sine and cosine terms

4.

The value of

e^{\infty}

is------------------

(a)

5.

The value of

e^{-\infty}

is------------------

(a)

6.

Laplace Transform transforms a function from

a)

$f\left(t\right)\ to\ F\left(s\right)$

b)

$F\left(s\right)\ to\ f\left(t\right)$

c)

$f\left(t\right)\ to\ f'\left(t\right)$

d)

$f"\left(t\right)\ to\ f'\left(t\right)$

7.

Which one is the correct definition of Laplace Transform?

a)

$F\left(s\right)=\int_0^{\infty}e^{-st}f\left(t\right)dt$

b)

$F\left(s\right)=\int_0^tf\left(t\right)g\left(t-u\right)$

8.

What is the Laplace Transform for $f\left(t\right)=t^3$ ?

a)

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

b)

$\frac{2}{s^3}$

c)

$\frac{6}{s^4}$

d)

$\frac{3}{s^3}$

9.

What is Laplace Transform for $e^{-2t}$ ?

a)

$\frac{1}{s-2}$

b)

$\frac{1}{s+2}$

c)

$\frac{2}{s}$

d)

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

10.

What is Laplace Transform for $\sin\ 2t$ ?

a)

$\frac{2}{s^2+2}$

b)

$\frac{s}{s^2+2}$

c)

$\frac{2}{s^2+4}$

d)

$\frac{s}{s^2+4}$

11.

What is Laplace Transform for $6\ \sin\ 2t$ ?

a)

$\frac{2}{s^2+4}$

b)

$\frac{s}{s^2+4}$

c)

$\frac{6}{s^2+4}$

d)

$\frac{12}{s^2+4}$

12.

Define this property: $L\left(f\left(t\right)e^{at}\right)=F\left(s-a\right)$

a)

Linearity Property

b)

First Shifting Property

c)

Convolution Theorem

d)

Second Shifting Property

13.

$L\left(e^{3t}t\right)$ Based on first shifting property, what is $a$ value?

a)

1

b)

2

c)

3

d)

4

14.

Find $L\left(e^{3t}t\right)$

a)

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

b)

$\frac{1}{\left(s-3\right)^2}$

c)

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

d)

$\frac{1}{\left(s\right)}$

15.

$L\left(e^{2t\ }\sin\ t\right)$ What is a and f(t)?

a)

$a=2,\ f\left(t\right)=e^{2t}$

b)

$a=4,\ f\left(t\right)=\cos\ t$

c)

$a=2,\ f\left(t\right)=\sin\ t$

16.

Find $L\left(\cos\ t\right)$

a)

$\frac{1}{s^2+1^{ }}$

b)

$\frac{1}{s^2+4}$

c)

$\frac{s}{s^2+1}$

17.

Find $L\left(e^{2t}\sin\ 2t\right)$

a)

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

b)

$\frac{s}{\left(s-2\right)^2+4}$

c)

$\frac{s}{\left(s-4\right)^2+1}$

18.

Find $L\left(t^3-3t^2+5t\right)$

a)

$\frac{6}{s^4}-\left(\frac{6}{s^3}\right)+\frac{5}{s^2}$

b)

$\frac{3}{s^3}-\left(\frac{1}{s^{\left(2\right)}}\right)+\frac{1}{s}$

c)

$\frac{2}{s^3}-\left(\frac{3}{s^{\left(2\right)}}\right)+\frac{5}{s}$

19.

Find $L\left(e^{3t}\left(t^3-3t^2+5t\right)\right)$

a)

$\frac{2}{\left(s-3\right)^4}-\left(\frac{3}{\left(\left(s-3\right)^3\right)}\right)+\frac{5}{\left(s-3\right)^2}$

b)

$\frac{6}{\left(s-3\right)^4}-\left(\frac{6}{\left(s-3\right)^3}\right)+\frac{5}{\left(s-3\right)^2}$

c)

$\frac{2}{\left(s-3\right)^3}-\left(\frac{3}{\left(s-3\right)^{\left(2\right)}}\right)+\frac{5}{s-3}$

20.

$L\left(t\ \cos\ 6t\right)$ Which Laplace property is use to solve this?

a)

Linearity Property

b)

Derivative of Laplace Transform

c)

First Shifting Property

d)

Second Shifting Property

21.

$L\left(t\ \sin\ 4t\right)$ What is n, f(t) and F(s)?

a)

$n=1,\ f\left(t\right)=\sin\ 4t,\ F\left(s\right)=\frac{s}{s^2+16}$

b)

$n=4,\ f\left(t\right)=t,\ F\left(s\right)=\frac{4}{s^2+16}$

c)

$n=1,\ f\left(t\right)=\cos\ 6t,\ F\left(s\right)=\frac{s}{s^2+14}$

22.

$Find\ L\left(t^{ }\sin\ 4t\right)$

a)

$\frac{2}{s^2+4}$

b)

$-\frac{4s}{\left(s^2+4\right)^2}$

c)

$-\frac{8s}{\left(s^2+16\right)^2}$

23.

$L\left(\sin^2t\right)$ What is $f\left(t\right),\ f'\left(t\right)\ and\ f\left(0\right)$ ?

a)

$f\left(t\right)=\sin^2t,\ f'\left(t\right)=2\ \cos t,\ f\left(0\right)=0$

b)

$f\left(t\right)=\sin^2t,\ f'\left(t\right)=\sin\ 2t,\ f\left(0\right)=0$

c)

$f\left(t\right)=\cos^2t,\ f'\left(t\right)=-\ \sin2t,\ f\left(0\right)=1$

24.

Find the Fourier Transform of an Exponential signal

f\left(t\right)=e^{-at}u\left(t\right),a>0

a)

$\frac{1}{a+jw}$

b)

$\frac{1}{a-jw}$

c)

$\frac{1}{-a+jw}$

d)

$\frac{1}{-a-jw}$

25.

Which of the following is the Analysis Equation of Fourier Transform?

a)

$F\left(w\right)=\int_{-\infty}^{\infty}f\left(t\right)e^{jwt\ }dt$

b)

$F\left(w\right)=\int_0^{\infty}f\left(t\right)e^{jwt}dt$

c)

$F\left(w\right)=\int_0^{\infty}f\left(t\right)e^{-jwt}dt$

d)

$F\left(w\right)=\int_{-\infty}^{\infty}f\left(t\right)e^{-jwt}dt$

26.

The Fourier Transform of a function

X\left(t\right)\ is\ X\left(w\right).

what will be the fourier transform of

\frac{\text{d}X\left(t\right)}{\text{d}t}

?

a)

$\frac{X\left(f\right)}{jf}$

b)

$j2\pi fX\left(f\right)$

c)

$\frac{\text{d}X\left(f\right)}{\text{d}t}$

d)

$jfX\left(f\right)$

27.

The Fourier Transform of a Gaussian Pulse is also a Gaussian pulse

a)

True

b)

False

28.

Find the Inverse Fourier transform of $\delta\left(w\right)$

a)

$\frac{1}{2\pi}$

b)

$2\pi$

c)

$\frac{1}{\pi}$

d)

$\pi$

29.

Find the inverse Fourier Transform of $f\left(t\right)=1$

a)

$u\left(t\right)$

b)

$\delta\left(t\right)$

c)

$e^{-t}$

d)

$\frac{1}{jw}$

30.

$f\left(x\right)=1,\ \ \ 0<x<\infty\$ cannot be represented by a Fourier Integral

a)

True

b)

False

SS- Revision 3

Total questions: 30

Worksheet time: 15mins

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