ECE 459: Communications I Problem Set 4 - Angle Modulation and FM Modulation, Assignments of Digital Communication Systems

Download ECE 459: Communications I Problem Set 4 - Angle Modulation and FM Modulation and more Assignments Digital Communication Systems in PDF only on Docsity! University of Illinois at Urbana-Champaign Department of Electrical and Computer Engineering ECE 459: Communications I Fall 2005 Problem Set 4 Angle Modulation, Phase and Frequency Modulation Issued: Thursday, Sept. 22nd. Due: Tuesday, October 4th (beginning of lecture). Reading from Lathi: Chapter 5 (excluding Section 5.5). Announcement: The first Mid-Semester Exam will be held on Thursday, October 6th, from 7-9pm in 165 Everitt. The exam will cover all material from the beginning of the term up to and including the lecture on Tuesday, September 27th. The corresponding material includes Problem Sets 1 through 4 and Chapters 1, 2, 3, 4 (excluding Sections 4.7–4.9) and 5 (excluding Section 5.5) from Lathi. During the exam, you can bring an 8.5 × 11-inch double-sided sheet of handwritten notes. Calculators are allowed but will not be necessary. A copy of an old exam is available for download from the course website. This exam does not necessarily resemble this year’s exam (also notice that the time allowed and the material covered in this old exam are slightly different from this year’s exam). Problem 4.1 (a) Problem 5.1-1 from Lathi, p. 248. (b) Problem 5.2-2 from Lathi, p. 249. Problem 4.2 Consider the FM signal s(t) = Ac cos [ ωct + kf ∫ t −∞ m(τ)dτ ] , where m(t) is the tone signal m(t) = Am sin(ωmt). The following parameters are given: Ac = 200V, ωc = 160π Mrad/s, kf = 20π Krad/(s Volt), Am = 1V, ωm = 16π Krad/s . (a) Find the frequency deviation ∆ω. (b) Find the modulation index β. (c) The narrowband FM signal approximation uses se(t) = Ac cos(ωct) − Ac [ kf ∫ t −∞ m(τ)dτ ] sin(ωct) as an approximation to s(t). Sketch |Se(ω)| and find its bandwidth.