Fourier series
Fourier series were developed by the French mathematician and scientist Joseph Fourier. Fourier wanted to understand how heat diffuses through materials and doing so required solving what is known as the Heat equation. Fourier discovered that solving the Heat equation was made easier if he expressed solutions as a sum of sine and cosine waves. In other words, Fourier decomposed the solution to make solving the equation easier. You will not be surprised to hear, given what we learned in the previous section, that sine and cosine waves are eigenfunctions of one of the operators in the Heat equation.
Since Fourier’s original work, using sine and cosine waves to decompose functions has been a standard tool in the toolkit of mathematicians and scientists. As data scientists, we shall learn about their usefulness as well.
Since we are using sine and cosine waves to decompose our function, , it won’t surprise you to learn that we use them to decompose periodic...