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Unformatted text preview: 1 Why sinusoids? “The method of calculation is considerably simplified. Whereas before we had to deal with periodic functions of an independent variable ‘time’, now we obtain a solution through the simple addition, subtraction, etc. of constant numbers … Neither are we restricted to sine waves, since we can construct a general periodic function out of its sine wave components … With the aid of Ohm’s Law in its complex form any circuit or network of circuits can be analysed in the same way, and just as easily, as for direct current, provided only that all the variables are allowed to take on complex values.” - C.P. Steinmetz Some Fourier series-square wave ) ( t x t A + A − 2 / T − 2 / T [ ] L + + + = ) / 10 sin( ) / 6 sin( ) / 2 sin( 4 ) ( 5 1 3 1 T nt T t T t t x π π π π m A f T 2 T 4 T 6 m θ f T 2 T 4 T 6 2 / π 2 / π − 1, 3, 5, 50 terms 2 Some Fourier series- triangle wave ) ( t x t A 2 / T − 2 / T ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + + + = L ) / 10 cos( ) / 6 cos(...
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- Fall '08
- Fourier Series, Periodic function, Square wave, Sine wave