Logarithms and Decibels

This appendix provides an introduction to logarithms (real and complex) and decibels, a quantitative measure of sound intensity. Several specific dB scales are defined, and dynamic range considerations in audio are considered.

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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
    • DBA (A-Weighted DB)
    • DB for Display
  • Dynamic Range
  
  
• Voltage, Current, and Resistance
• Exercises

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.