**Unformatted text preview: **1* {El 1111, 11m] is the f and discrete time till
1stem output consis,
o-input response. ___E
incrementally line.
inearly to changesii.
any two inputs to .111
eons) function of _
are two inputs to E1: .-.i
[responding outpuf, :1[11]} . (1.13.“ :o continuous-ti 1111..
ive picture of w__=_1.
representation f11.
ly, we introducivz'
PEiPI'emutations-121511
red and examin-‘r-
:se included co 11:1.
1functions. In it“
and discrete-ti;_.f1_,1i'ii 1 introduced
5 systems, and -_-1;1;1
ity, stability, 11' 11;: 1ar, tirne—invari'n
stems play a
he fact that 1
11d time invari
linearity and tire-1. 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 ...

View
Full Document

- Spring '09
- buyurman