concept square wave in category python

This is an excerpt from Manning's book Math for Programmers: 3D graphics, machine learning, and simulations with Python MEAP V11. Login to get full access to this book.

If you zoom out, you can see that this Fourier series comes close to the square wave we plotted at the beginning of the chapter (figure 13.24).

Figure 13.24: The first 50 non-zero terms of the Fourier series are close to a square wave, like the first function we met in this chapter.

What we’ve done here is to build an approximation of the square wave function as a linear combination of sinusoids. It’s counterintuitive that we can do this! After all, all of the sinusoids in the Fourier series are round and smooth, and the square wave is flat and jagged. We’ll conclude this chapter by showing how to reverse engineer this approximation, starting with any periodic function and recovering the coefficients for a Fourier series that approximates it.