Properties of DB Scales

In every kind of dB, a factor of 10 in amplitude increase corresponds to a 20 dB boost (increase by 20 dB):

and , of course. A function which is proportional to is said to ``fall off'' (or ``roll off'') at the rate of dB per decade. That is, for every factor of in (every ``decade''), the amplitude drops dB.

Similarly, a factor of 2 in amplitude gain corresponds to a 6 dB boost:

and

A function which is proportional to is said to fall off dB per octave. That is, for every factor of in (every ``octave''), the amplitude drops close to dB. Thus, 6 dB per octave is the same thing as 20 dB per decade.

A doubling of power corresponds to a 3 dB boost:

and

Finally, note that the choice of reference merely determines a vertical offset in the dB scale:

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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.