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.
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: ^{1}^{2}
Simulate approximates the following waves:
 Sawtooth function
 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 ‘a_{n}’ and ‘b_{n}’

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