O'Reilly logo

The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

VII.03 Wavelets and Applications

Ingrid Daubechies

1 Introduction

One of the best ways to understand a function is to expand it in terms of a well-chosen set of “basic” functions, of which TRIGONOMETRIC FUNCTIONS [III.92] are perhaps the best-known example. Wavelets are families of functions that are very good building blocks for a number of purposes. They emerged in the 1980s from a synthesis of older ideas in mathematics, physics, electrical engineering, and computer science, and have since found applications in a wide range of fields. The following example, concerning image compression, illustrates several important properties of wavelets.

2 Compressing an Image

Directly storing an image on a computer uses a lot of memory. Since memory is ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required