NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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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Logarithms, Decibels, and Number Systems
This chapter provides an introduction to logarithms (real and complex),decibels, and number systems such as binary integer fixed-point, fractional fixed-point, one's complement, two's complement, logarithmic fixed-point,-law, and floating-point number formats.
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- Linear Number Systems for Digital Audio
- Pulse Code Modulation (PCM)
- Binary Integer Fixed-Point Numbers
- Fractional Binary Fixed-Point Numbers
- How Many Bits are Enough for Digital Audio?
- When Do We Have to Swap Bytes When Changing Computers?
- Logarithmic Number Systems for Digital Audio
- Appendix A: Round-Off Error Variance
- Appendix B: Electrical Engineering 101