NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University
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Logarithmic Number Systems for Digital Audio
Since hearing is approximately logarithmic, it makes sense to represent sound samples in a logarithmic or semi-logarithmic number format.Floating-point numbers in a computer are partially logarithmic (the exponent part), and one can even use an entirely logarithmic fixed-pointnumber system. The -law amplitude-encoding format is linear at small amplitudes and becomes logarithmic at large amplitudes. This section discusses these formats.