University of South Australia EEET 3028 2013sp6 (013388) Introduction to Communication Systems School of Engineering Assignment 1: Signals & Spectra, Filtering, and Amplitude Modulation Due date: 11 pm, 13th October 2013 General Information: Each task consists of: 1. A set of tutorial/exam type problems, which you will need to solve with pen and paper. 2. A set of simulation tasks in MATLAB related to the specific questions. This document and all required files are available for downloading from the learn online course web page. Final Report and Evaluation Your report should consist of: • Solutions to the problems (including mathematical derivations). • A working copy of the MATLAB code. • All the plots generated in MATLAB, with appropriate title description. (You can add the titles to the plots in the report document after copying them to your document, if that is easier). Evaluation will be based on the components above. Hand-written solutions to the problems are to be scanned into a pdf file, to which you will attach the plots and the MATLAB code. Note: Hand-written answers/mathematical derivations will be accepted only if done neatly and clearly. You may scan them and submit electronically. Assignment 1: Signals & Spectra, Filtering, and Amplitude Modulation Page 1 of 4
University of South Australia EEET 3028 2013sp6 (013388) Introduction to Communication Systems School of Engineering Task 1: Fourier Series Let fc > 0. Consider the half-wave-rectified cosine wave, a periodic signal defined as: v(t) = Ac max??cos(2fct), 0. 1. Sketch this signal. What is the period T0 of this signal? 2. Find the average value and the power of this signal by integrating 1 T0 v(t) and 1 T0 v2(t) respectively in the time domain, over one period. Your answer must be expressed in terms of fc and Ac only. 3. Derive and show that the Fourier coefficients of the above signal v(t) are given by: cn =??? ?? Ac (-1)n2 -1 n2-1 , n even Ac 4 , n = ±1 0 , n odd and n 6= ±1. Hint: sinn – 1 2 =…