NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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

<< Previous page  TOC  INDEX  Next page >>

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.

FIXME: HERE HERE HERE

---

Subsections

• Logarithms
  • Changing the Base
  • Logarithms of Negative and Imaginary Numbers
• Decibels
  • Properties of DB Scales
  • Specific DB Scales
    • DBm Scale
    • DBV Scale
    • DB SPL
    • DB for Display
  • Dynamic Range
• Linear Number Systems for Digital Audio
  • Pulse Code Modulation (PCM)
  • Binary Integer Fixed-Point Numbers
    • One's Complement Fixed-Point Format
    • Two's Complement Fixed-Point Format
    • General Formula for Two's-Complement, Integer Fixed-Point Numbers
    • ''Little Endian'' Formula for Two's-Complement, 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
  • Floating-Point Numbers
  • Logarithmic Fixed-Point Numbers
  • -Law Companding
• Appendix A: Round-Off Error Variance
• Appendix B: Electrical Engineering 101

<< Previous page  TOC  INDEX  Next page >>