w03-p2-fourier-series-2up

# w03-p2-fourier-series-2up - Week 03 Part2 Fourier Series...

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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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w03-p2-fourier-series-2up - Week 03 Part2 Fourier Series...

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