Decibels

A decibel (abbreviated dB) is defined as one tenth of a bel. The bel^F.1 is an amplitude unit defined for sound as the log (base 10) of the intensity relative to some reference intensity,^F.2 i.e.,

The choice of reference intensity (or power) defines the particular choice of dB scale. Signal intensity, power, and energy are always proportional to the square of the signal amplitude. Thus, we can always translate these energy-related measures into squared amplitude:

Since there are 10 decibels to a bel, we also have

A just-noticeable difference (JND) in amplitude level is on the order of a quarter dB. In the early days of telephony, one dB was considered a reasonable ``smallest step'' in amplitude, but in reality, a series of half-dB amplitude steps does not sound very smooth, while quarter-dB steps do sound pretty smooth. A typical professional audio filter-design specification for ``ripple in the passband'' is 0.1 dB.

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Subsections

• Properties of DB Scales
• Specific DB Scales
  • DBm Scale
  • DBV Scale
  • DB SPL
  • DBA (A-Weighted DB)
  • DB for Display
  
  
• Dynamic Range

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Order a Hardcopy of Mathematics of the DFT

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Next: Properties of DB Scales

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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.