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Drawing with Fourier Transform and Epicycles
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Here is a geometric way to draw a Fourier series. Instead of writing sines and cosines as equations, each term of the Fourier series is shown as a rotating circle (an epicycle). 1. Each circle = one harmonic • The first (largest) circle rotates at the fundamental frequency. • The next circles rotate at 3×, 5×, 7×, … the frequency (square waves only use odd harmonics). • Each circle’s radius equals the Fourier coefficient for that harmonic. So large circles matter more; small ones add fine detail
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