Math for Programmers

13 Analyzing sound waves with a Fourier series

This chapter covers

• Defining and playing sound waves with Python and PyGame
• Turning sinusoidal functions into playable musical notes
• Combining two sounds by adding their sound waves as functions
• Decomposing a sound wave function into its Fourier series to see its musical notes

For a lot of part 2, we’ve focused on using calculus to simulate moving objects. In this chapter, I’ll show you a completely different application: working with audio data. Digital audio data is a computer representation of sound waves, which are repeating changes of pressure in the air that our ears perceive as sound. We’ll think of sound waves as functions that we can add and scale as vectors, and then we can use integrals ...