# 1 - 1{El 1111 11m is the f and discrete time till 1stem...

• Essay
• 1

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern