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Fourier Series


A Fourier transform is a way of breaking down a complex function into (infinite) sums of sine and cosine waves. In short, given a smoothie, it finds its recipe. Fourier series is the Fourier transform of a periodic function and it aims to represent the periodic function as a sum of sinusoidal waves. It is analogous to the Taylor series, which represents functions as an infinite sum of monomial terms.

S_{n}(x) = \frac{a_{o}}{2}+\sum_{n=1}^{N}(a_{n}\cos(\frac{2\pi nx}{P}) + b_{n}\sin(\frac{2\pi nx}{P}))

This sum of sine and cosine waves can also be thought of as a list of phasors. Hence, the Fourier series generates a list of phasors which, when summed together, reproduces the original signal. The below animation shows how this can look like: 12

FourierSeriesPhasors FourierSeriesPhasors

Simulate approximates the following waves:

  1. Sawtooth function
  2. Square function

We have the flexibility to fiddle with the following parameters:

  • N: The number of phasors (sine and cosine terms) generated

  • Amplitude: The coefficients ‘an’ and ‘bn

  • Frequency: The value of ‘n’ to adjust the frequency of sine and cosine terms



Last update: December 25, 2021