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Unformatted text preview: h old, t he signals are functions of space a nd time; such a system is a
d istributedparameter system.
6. S ystems w hose inputs a nd o utputs a re continuoustime signals are continuoustime systems; systems whose inputs and o utputs are discretetime signals are
discretetime systems. I f a continuoustime signal is sampled, t he resulting
signal is a d iscretetime signal. We can process a continuoustime signal by
processing t he samples of this signal with a discretetime system.
7. S ystems w hose inputs a nd o utputs a re analog signals are analog systems; those
whose i nputs a nd o utputs are digital signals are digital systems.
8. I f we c an o btain t he i nput / (t) back from t he o utput y (t) of a system S by
some o peration, t he system S is s aid to be invertible. Otherwise t he system is
n oninvertible.
T he s ystem model derived from a knowledge of t he i nternal s tructure of the
system is its i nternal description. In contrast, a n external description of a system
is i ts description as seen from t he s ystem's i nput a nd o utput terminals; it can be
obtained by a pplying a known input a nd measuring the resulting o utput. I n t he
m ajority of p ractical systems, a n e xternal description of a system so obtained is
equivalent t o i ts i nternal description. In some cases, however, t he e xternal description fails t o give adequate information a bout t he system. Such is t he case with t he
socalled uncontrollable or unobservable systems. References
1. 2.
3.
4. P apoulis, A ., T he Fourier Integral and Its Applications, McGrawHill, New
York, 1962.
K ailath, T ., L inear Systems, PrenticeHall, Englewood Cliffs, New Jersey, 1980.
L athi, B .P., Signals, Systems, and Communication, Wiley, New York, 1965.
Lathi, B .P., Signals and Systems, BerkeleyCambridge Press, Carmichael, California, 1987. Problems
Find the energies of the signals illustrated in Fig. P I.II. Comment on the effect on
energy of sign change, time shifting, or doubling of the signal. What is the effect on
the energy if the signal is multiplied by k?
1 .12 Repeat Prob. 1.11 for the signals in Fig. P1.12.
1 .13 ( a) Find t he energies of the pair of signals x (t) and y(t) depicted in Figs. P l.l3a
and b. Sketch and find the energies of signals x (t) + y(t) and x (t)  y(t). Can you
make any observation from these results? 97 Problems
(b) (a) ( d) (c) sintr\ F ig. P l.ll
f (t) 0 O t ~
o 2 t f 3 ( t) 1 o 2 t 0 1 F ig. P l.l2 x (t) ~
o 0 2 (a) x (t) 0 1 1 1 1 y (l) t 0 I (b) x (t)
y (t) 1 .11 I (c) 0 It I Fig. P l.l3
( b) Repeat part (a) for the signal pair illustrated in Fig. P1.13e. Is your observation
in p art (a) still valid? 98
1 .14 1 I ntroduction t o S ignals a nd S ystems 99 P roblems F ind t he p ower o f t he p eriodic signal f (t) s hown in Fig. P1.14. F ind also t he powers
a nd t he r ms values of: ( a)  f(t) ( b) 2 f(t) ( c) c f(t). C omment. f (1) 0.5 o 1 24 I ..... t F ig. P 1.32 Fig. P l.l4
1 .15 S how t hat t he p ower o f a signal
1 n f (t) = L Dke jwkt is Fig. P 1....
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 Spring '13
 Bayliss
 Signal Processing, The Land

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