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Logarithmic Number Systems for 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-point number system. The $ \mu$ -law amplitude-encoding format is linear at small amplitudes and becomes logarithmic at large amplitudes. This section discusses these formats.



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``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 © 2014-04-06 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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