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Unformatted text preview: Week 03: Part2: Fourier Series * Main Text: Signal Processing First, J. H. McClellan, R.W. Schafer & M.A. Yoder ECTE906 Advanced Signals & Systems Master of Engineering Studies Parviz Doulai SECTE/Spring Session 2009 This document makes use of an earlier document prepared by D. Sutanto Main Source: The subject textbook as well as the following URL; http://users.ece.gatech.edu/mcclella/SPFirst/LectureSlides/SPFirstLectureSlides.html Page 2 ECTE906 Advanced Signals & Systems Spring 2009 Background: Spectrum of a Signal sine signals are the basic building blocks for making more complicated signals. The common method for producing new signals from sinusoids is the additive linear combination where a constant and several sinusoids (with different frequency, phase and amplitude) are added to make a new signal. Summing several sine signals of the same frequency but arbitrary amplitudes and phases produces a new single sinusoid of the same frequency, and Summing several sinusoids of different frequencies will produce a waveform that is no longer purely sinusoidal. The spectrum of a signal is a graphical representation of the frequency components it contains, and their complex amplitudes. Page 3 ECTE906 Advanced Signals & Systems Spring 2009 Examples: Frequency Spectrum A voice waveform and its frequency spectrum Source: wiki A triangle wave: time and frequency domains. The fundamental frequency component is at 220 Hz Source: wiki Page 4 ECTE906 Advanced Signals & Systems Spring 2009 Fourier Series & Fourier Analysis A Fourier series decomposes a periodic function (signal) into a sum of simple oscillating functions, namely sines and cosines (or complex exponentials). The Fourier Series has many applications in electrical engineering, vibration analysis, acoustics, optics, signal processing, image processing, quantum mechanics, etc. The study of Fourier series is a branch of Fourier analysis. Page 5 ECTE906 Advanced Signals & Systems Spring 2009 In mathematics, a Fourier series decomposes a periodic function or periodic signal into a sum of simple oscillating functions, namely sines and cosines (or complex exponentials). The study of Fourier series is a branch of Fourier analysis....
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