Number Systems for Digital Audio

This appendix discusses number formats used in digital audio. They are divided into ``linear'' and ``logarithmic.'' Linear number systems include binary integer fixed-point, fractional fixed-point, one's complement, and two's complement fixed-point. The -law format is a popular hybrid between linear and logarithmic amplitude encoding. Floating-point combines a linear mantissa with a logarithmic ``exponent,'' and logarithmic fixed-point can be viewed as a special case of floating-point in which there is no mantissa. This appendix does not cover audio coding methods such as MPEG (MP3) [4,6,48,5] or Linear Predictive Coding (LPC) [9,38,39].

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Subsections

• Linear Number Systems
  • Pulse Code Modulation (PCM)
  • Binary Integer Fixed-Point Numbers
    • One's Complement Fixed-Point Format
    • Two's Complement Fixed-Point Format
    • 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?
  
  
• Logarithmic Number Systems for Audio
  • Floating-Point Numbers
  • Logarithmic Fixed-Point Numbers
  • Mu-Law Coding
  
  
• Round-Off Error Variance

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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.