Abstract: Out of all the image formats out there, JPEG is the most widely used in the world, and for good reason: they allow us to send and upload images at a reduced size without losing most details of an image. But how does it do this? It turns out that the JPEG algorithm is highly related to discrete Fourier analysis, and gives a great excuse to talk about important topics in math. In particular, the JPEG algorithm takes advantage of information in the frequency domain, strategically “discretizing” higher frequencies. In this activity, we’ll interactively explore the basics of (discrete) Fourier analysis and its applications, applying them to signals, image analysis, and beyond.