18.03 Lecture Notes - Periodic Function, Fourier Series, Constant Function
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[1] periodic functions: for example the heartbeat, or the sound of a violin, or innumerable electronic signals. I showed an example of somewhat simplified waveforms of a violin and a flute. A function f(t) is "periodic" if there is l > 0 such that f(t+2l) = f(t) for every t . So strictly speaking the examples given are not periodic, but rather they coincide with periodic functions for some period of time. Our methods will accept this approximation, and yield results which merely approxmimate real life behavior, as usual. The constant function is periodic of every period. Otherwise, all the periodic functions we"ll encounter have a minimal period, which is often called the period. Any "window" (interval) of length 2l determines the function. We"ll often use the window [-l,l] . (this is one reason why chose to write the period as 2l. ) [2] sine and cosines are basic periodic functions.
