Compressing audio signals with interactive and cloud-based learning material—a workshop for high-school students

Abstract

Abstract Undeniably omnipresent in our everyday lives, electronic signal compression is a classical example that illustrates the ubiquity of mathematics in high-end technology and sciences. When dealing with piles of files, it is essential that each file takes up as little storage space as possible while maintaining quality. The cloud-based—available under a Creative Commons licence—workshop that is described in the following paper addresses this trade-off between quality and compression rate based on the example of audio signals. Here, students use tools from linear algebra to compress music according to their own hearing model which they developed previously. More specifically, they use the basis change (i.e. the Fourier transform) between the time-dependent and frequency-dependent representations of sounds to remove those frequencies from an instrumental piece that are outside of their hearing model. Such mathematical tools may seem out of reach for high-school students, but we demonstrate that they are indeed suited for developing solutions with minimal help.