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any two inputs to .111
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are two inputs to E1: ..i
[responding outpuf, :1[11]} . (1.13.“ :o continuousti 1111..
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ity, stability, 11' 11;: 1ar, tirne—invari'n
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linearity and tire1. Chap. 1 1.} ( ® [@11 Problems Basic problems emphasize the mechanics of using concepts and methods in a man ner similar to that illustrated in the examples that are solved in the text. Advanced problems explore and elaborate upon the foundations and practical im— plications of the textual material. . The ﬁrst section of problems belongs to the basic category, and the answers are pro
vided in the back of the book. The next two sections contain problems belonging to the
basic and advanced categories, respectively. A ﬁnal section, Mathematical Review, pro—
vides practice problems on the fundamental ideas of complex arithmetic and algebra. o+rﬁt a1mm=wxwm
(oxms=drum (a :1:[11  3]
“(é x[*n + 2] (a) x(1 — r)
('1) M31?) BASIC PROBLEMS WITH ANSWERS @ x201) : gjl2t+1irl4ji (e) leﬂl : ej(srl2n+w1’8) (C) xlnn] 1.2. Express each of the following complex numbers in polar form (reiﬁ, with —sr <
19 E 11')15.—2.—3.1. E  17E 1 +J1(1‘“J)21 10:1?) (1.f_i_)_[(1_~—1).(_\/§ + Jﬁy 1.3. Determine the values of P111 and E111 for each of the following signals: (1;) 1:30?) = 1:050?)
(”5) win] = 008$”) QM= Let x[a] be a signal with x[r1] = 0 for a < —2 and n :21 4. For each signal given
. ' below, determine the values of 111 for which it is guaranteed to be zero. (1)) x[n + 4]
(e) Il—H _ 2]
._ kLet .110) be a signal with x0) = 0 for r «I. 3. For each signal given below, determine
\J the values of t for which it is guaranteed to be zero. (b) x(1 — I) + x(2 — r)
ﬁr?) x(t/ 3)
ermine whether or not each of the following signals is periodic:
x10“) 2 Zeiii+Wi4)a(t)
@3‘1131111 = ::=_,{5[11 — 4k] _ am — 1 — 411]}
1.7. For each signal given below, determine all the values of the independent variable at (c) in — 11142 — 1) (prpmrzan+uhn N.
xx /
x, __ which the even part of the signal is guaranteed to be zero. (3) Min] = 11[11] — .ulﬂ _ 4]
. sammi=eran—n
1.8. Express the real part of each of the following signals in the form Arr—iii cos(wt + d1), (11) 212(1) = SM?)
((1) 111(1) = (5:110:41 2) where A, a, to, and (i: are real numbers with A > Gland —qr < qb E qr:
(11) 112(1) : ﬂew“ 1103(3): + 2111) (a) J1310') = “2  ((1) x30“) = e‘isin(3t + a")
 @ Determine whether or not each of the following signals is periodic. If a signal is
periodiis, specify its fundamen .eam=jwm (ﬂ‘i x11[r1] = 3ej3ﬁln+li2)i5 tal period. ‘bi I : (_l‘i‘j)!
((123 gig] =€38j3lﬁln+li21 (d) 364(3) = je(—2+j100}r...
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 Spring '09
 buyurman

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