Sample Exam 2: Chapters 1, 2, and 3
#1) Consider the linear-time invariant system represented by
iBjklKm
il n
jklmFoqprYs9kltumvgjkxwymFoqw
Find the system response and its zero-state and zero-input components. What are the response steady
state and transient components.
#2a) Using the properties of the impulse delta signal simplify the following expressions
kz+mkl t{m|}kl=tH{mvHkzz+m~
~
pfklKm+}""kl tS{&m+il>vHkzzz+m
|
~
prYs9k+(lm}ku&l=tm+il
kzm
~
4
prs9ku&l>m}kl=tDum+ilv kmq
klm}K"kl
nH
mil
#2b) Plot the graph of the signal represented in terms of unit step, rectangular, and unit ramp
signals as
klmFoqkltDum
n
klt
m tDktUl
n
ym
and find its generalized derivative.
#3a) Find the Fourier series for the sawtooth signal with
o{vK¡oN{
. Note it is an odd signal.
Hint:
lyprYs9k¢l>milo
{
¢
|
prYs9k¢lmt
l
¢
>
p(k¢l>m
#3b) Find the liner system response due to the periodic input signal defined in 3a). The system
transfer function is
£
k¤Um¥o ¦§
K¨
¦§
.
#3c) Using the tables of common pairs and properties of the Fourier transform find Fourier transforms
of the following signal:
kz"m©prYs9k+lKm"ª«f¬kl=tm tf¬kl=tS{®m¯vgk+zzm_l
|
@¬klKm>v°kzzzm$prs
ku&l=tDm
#3d) Find the inverse Fourier transform of the signal
±
kY²¤³mFoq´
k¤Um tµ
|
k¤t{m
#3e) Find the response of the system defined in 3b) due to the input signal
>
pF¶"{awl
n¸·
@¹
.
2
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