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Unformatted text preview: Boise State University Department of Electrical and Computer Engineering ECE 225 Circuit Analysis and Design Fourier Series Lecture Objectives : 1. To review the Fourier series expansion of periodic waveforms. 2. To discuss the computation of Fourier coefficients by taking advantage of waveform sym- metries (even-function symmetry, odd-function symmetry, half-wave symmetry, and quarter- wave symmetry). o f(t ) t + T o o t f(t) t T Introduction : Periodic functions occur frequently in engineering problems. Some of these functions may be discontinuous such as square waveforms. These functions can be represented in terms of simple sine and cosine functions leading to Fourier series, named after the French physicist Joseph Fourier (1768-1830). Periodic Function : A function f ( t ) is said to be periodic if it defined for all t and there exists a positive number T called the period such that f ( t + T ) = f ( t ) for all t In other words, such a function repeats itself every T seconds. Notice that, if n is an integer, then f ( t + nT ) = f ( t ) for all t so that any integral multiple of T is also a period. The smallest such number T is called the fundamental period and f = 1 /T in hertz (Hz) is called the fundamental frequency. Trigonometric Fourier Series : f ( t ) = a o + a 1 cos t + a 2 cos2 t + ... + a n cos nt + ... + b 1 sin t + b 2 sin2 t + ... + b n sin nt + ... The class of periodic functions which can be represented by Fourier series is surprisingly large and general. The following sufficient conditions cover almost any conceivable engineering application....
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- Fall '08