Overview

Most everyone watches television or listens to the radio, and many people use the Internet to obtain graphic images, sound, and video. How can this information be transmitted electronically without requiring an immense amount of time and space? The FBI has accumulated approximately 200 million fingerprint files. How can a current suspect's fingerprints be compared with the contents of these files? The answer is harmonic analysis, which allows us to compress these images and sounds into their main components before transmission, and reconstruct them on the receiving end. Harmonic analysis grew out of a study of the way a string vibrates, and continues to reinvent itself. Harmonic analysis bridges the gap between mathematical theory and engineering practice.

Background

In Recherches sur les cordes vibrantes (1747), the French mathematician Jean d'Alembert (1717-1783) described his study of the shape of a vibrating string fixed at...