Introduction

Abstract

We hear a sound and we want to store it for later replay — what information do we need to capture? Physicists tell us that sound is a pressure wave (i.e., vibration) in the air so we can measure this pressure wave with a mechanical device and then mechanically reproduce the pressure wave later. This is the principle used by Thomas Edison and other manufacturers of early gramophones (precursors to phonographs) in which a large cone concentrated the vibrations to a point where a needle scratched its vibrating path onto a spinning cylinder or disk. Later, a hand-cranked or other form of motor would turn the spinning cylinder or disk and the needle’s forced movement along its prior path would cause the cone to recreate the pressure wave. The advent of electronic technology has allowed us to convert the pressure wave into a voltage reading that can be transferred onto a variety of storage media, for example as a changing degree of magnetization along a cassette tape. The basic idea in analogue technology, however, is still the same — to represent sound by the amplitude of its vibration over time. This tells us that one basic representation of sound is as a changing function of time t, which we denote x(t) as shown in Figure 1.