ES240_FourierSeries

ES240_FourierSeries - ES 240: Scientific and Engineering...

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ES 240: Scientific and Engineering Computation. Introduction to Fourier Series Trigonometric Fourier Series Trigonometric Fourier Series Outline Introduction Visualization Theoretical Concepts Qualitative Analysis Example Class Exercise
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ES 240: Scientific and Engineering Computation. Introduction to Fourier Series Introduction Introduction What is Fourier Series? Representation of a periodic function with a weighted, infinite sum of sinusoids. Why Fourier Series? Any arbitrary periodic signal, can be approximated by using some of the computed weights These weights are generally easier to manipulate and analyze than the original signal
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ES 240: Scientific and Engineering Computation. Introduction to Fourier Series Periodic Function Periodic Function What is a periodic Function? A function which remains unchanged when time-shifted by one period f(t) = f(t + T o ) for all values of t What is T o T o T o
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ES 240: Scientific and Engineering Computation. Introduction to Fourier Series Properties of a periodic function 1 Properties of a periodic function 1 A periodic function must be everlasting From –∞ to ∞ Why? Periodic or Aperiodic?
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ES 240: Scientific and Engineering Computation. Introduction to Fourier Series Properties of a periodic function Properties of a periodic function You only need one period of the signal to generate the entire signal Why? A periodic signal cam be expressed as a sum of sinusoids of frequency F 0 = 1/T 0 and all its harmonics
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ES 240: Scientific and Engineering Computation. Introduction to Fourier Series Visualization Visualization Can you represent this simple function using sinusoids? Single sinusoid Single sinusoid representation representation
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ES 240: Scientific and Engineering Computation. Introduction to Fourier Series Visualization Visualization
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This note was uploaded on 09/04/2011 for the course ES 240 taught by Professor Dr,uche during the Spring '11 term at Montgomery College.

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ES240_FourierSeries - ES 240: Scientific and Engineering...

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