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Using the Shannon Sampling Theorem to Design Compact Discs (UMAP)

Susan E. Kelly


Mathematics Topic:
Article, Calculus, Trigonometry
Application Areas:
Music, engineering

| ©2000 by COMAP, Inc. | The UMAP Journal 21.2 | 10 pages |


Have you ever wondered how music is stored on a compact disc and then reproduced? Mathematically, the music can be viewed as a function in time. To record the music on a disc, the function is converted to a series of numbers that represent the function’s amplitude at evenly spaced points in time. These numbers are what are stored on the disc. The Shannon Sampling Theorem explains how many amplitude readings are needed and how these numbers are used as the coefficients of a series that will reproduce the music. To understand this theorem, we first examine a small amount of complex number theory and some Fourier analysis. We then see how the Shannon Sampling Theorem is applied to the design of compact discs and players.

Table of Contents:

ABSTRACT

INTRODUCTION

BACKGROUND IN COMPLEX NUMBERS

FOURIER ANALYSIS

SHANNON SAMPLING THEOREM

STORING INOFRMATION ON A COMPACT DISC

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHOR