CONFIDENTIAL

$r {4

{"H3

UNIVERSITI TUN HUSSEIN ONN MALAYSIA

FINAL EXAMINATIONSEMESTERII

SESSION 2012t2013

COTIRSE NAME : SIGNALS AND SYSTEMS

COURSECODE : BEB 20203

PROGRAMME : BEB

EXAMINATION DATE : JUNE 2013

DURATION : 3 HOURS

INSTRUCTION : ANSWER FIVE (5) QUESTIONSONLY

THIS QUESTION PAPER CONSISTS OF SEVEN (7) PAGES

CONFIDENTIAL

BEB 20203

Ql (a) Prove the r(t) glven below is a periodic signal. Then, calcurate thefundamental period.

.rG) =:cosJ Sr+1 I\ 6,/

Airr: For any integer value of M, cos(e +ZAW)= e6sg

(6 marks)

(b) A cortinuous-time signal is given ?,s x(t) = 3 + 2t + 51. Examme the Evenand Odd part ofthe signal above.

(8 marks)

(c) Given the continuous -time signal x(t), as depicted in Figure el. Illustrate:

(D x"O = 2x(t)

(iD xb(t) = x(2t). (3 marks)

(3 marks)

Q2 (a) State whether the following systems are time invariant or not.

(D yO : 3re)

(iD yO = 3j0)

(8 marks)

(b) Test the following systems for linearity.

(i) y(t) = t x(t)

(i, y(t) = x,(,(8 marks)

(c) civen that v(t) = x(t) + 2x(3 - t). Distinguish th€ causality ofthe sy.l?i_*l

Q3

Q4

(b)

(al

(a)

BEB 20203

D€termine the trigonometdc form of Fourier series ofthe waveform shown inFigure Q3.

( l4 marks)

For an Exponential form Fourier series 4 it

For a gi ven var ue A = r0. pr",,h" d*br:r"j;'.t"ffi i*11" =.r,1*

diagram for a given value ofn fiom -3 to 3

(6 ma*s)

Fourier Transform gives an unique and powerful way to view electromasnelicwavetoftn such as sound waves. satellite broadcasting signal etc. defineFourier Transform ofa continuous-time signal, rfr.

(6 marks)

By.using the,Fourier Transform, calculate the convolution of rL = e.2'u(t)and, x2O = e'o'u(t).

( 14 marks)

The impulse response ofa system is given as;

h(t) = 2e'' u(t)

By using Fourier Transform, formulate the response of the system for giveninpt x141 =2"'" u111.

( l0 marks)

Let x(t) = eat u(t), wherc a > 0 and

= e-'' for t 2 0.

By using Laplace Transfom, plot the Region of Convergence (ROC) diagram.

(b)

(a)Q5

(b)

(10 mdks)

BEB 20203

Q6 (a) By referring to Figurc Q6, calculate the Laplace Transform of that periodicsquarc wave.

(10 marks)

(b) The impulse response ofa system is given as;

h(t) = (2 + t) e-r'u(t)

Evaluate the transfer function of the system above.( l0 narks)

- END OF QUESTION -

4

BEB 20203

SEMESTER./SESSIONCOURSE NAME

FINAL EXAMINATION

I sEM II / 2012/2013: SIGNALS AND SYSTEMS

PROGRAMME : BEBCOURSE CODE |BEB 20203

ll

FICURE 01

FIGI,IRX 03

BEB 20203

SEMESTEPJSESSIONCOURSE NAME

FINAL EXAMINATION

: sEM II / 201212013: SIGNALS AND SYSTEMS

PROGRAMME : BEBCOURSE CODE : BEB 20203

FIGURE 06

BEB 2O2OJ

FINAL EXAMINATION

SEMESTER/SESSION : SEMII / 2O12^OB pROCRAMME |BEBCOURSE NAI\,'E : SIGNALS AND SYSTEMS COWSi COOE . ggS ZOZO:

Some useful Laplace Tratrsform pairs

l) Lte''u(r)l= -L.111u1,11 = -Ls+a s,

z) IfL{xO} = x(s), then L {e-atx(t)} = X(sfa)

3) s=o+jo

Fourier Transform

l) F{e a'u(t)}= , ^

J@+A