Ve216LectureNotesChapter3Part2

Ve216LectureNotesChapter3Part2 - Ve216 Lecture 10 Dianguang...

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Unformatted text preview: Ve216 Lecture 10 Dianguang Ma Spring 2008 Chapter 3 (Part II) Fourier Representations of signals and LTI Systems 3.5 The Fourier Series Example 3.14 Square-wave partial-sum approximation: In 1898, an American physicist, Albert Michelson, constructed a harmonic analyzer, a device that, for many periodic signals, would compute the truncated FS approximation for values of J up to 80. - = = J J k t jk J e k X t x ] [ ) ( 3.5 The Fourier Series Michelson tested his device on many functions, with the expected result that truncated FS approximation looked very like x(t). However, when he tried the square wave, he obtained an important and, to him, very surprising result. Michelson was concerned about the behavior he observed and thought that his device might have had a defect. He wrote about his problem to the famous mathematical physicist Josiah Gibbs, who investigated it and reported his explanation in 1899. 3.5 The Fourier Series What Michelson had observed is illustrated in Figure 3.25 - The partial-sum approximation of the square wave that has period T = 1 and T /T=1/4. 3.5 The Fourier Series What Michelson had observed is illustrated in Figure 3.25 - The partial-sum approximation of the square wave that has period T = 1 and T /T=1/4. 3.5 The Fourier Series What Michelson had observed is illustrated in Figure 3.25 - The partial-sum approximation of the square wave that has period T = 1 and T /T=1/4. 3.5 The Fourier Series What Michelson had observed is illustrated in Figure 3.25 - The partial-sum approximation of the square wave that has period T = 1 and T /T=1/4. 3.5 The Fourier Series3....
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This note was uploaded on 10/26/2009 for the course EECS EECS 216 taught by Professor Dianguangma during the Spring '09 term at University of Michigan-Dearborn.

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Ve216LectureNotesChapter3Part2 - Ve216 Lecture 10 Dianguang...

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