Here are two items I found on the net re decibels:
1) The Decibel
The decibel (dB) is one tenth of a Bel, a unit for comparing two
power or sound intensity levels. Decibels are used for most purposes. The decibel
represents about the smallest change in sound intensity level that the human ear can
detect. As it is a unit of comparison, an intensity given in decibels means nothing
unless we know what the level is being compared with. So a level should be given
as being so many decibels above or below some reference, or 'zero' level.
We often compare the level of a sound with the intensity at which it
would only just be audible. We would then say that the sound was so many
decibels above the threshold of hearing. About 120 decibels above this level, the
sensation of hearing starts to change to one of pain.
2) What is a Decibel?
Decibel is the unit used to express relative differences in signal
strength. It is expressed as the base 10 logarithm of the ratio of the powers of two signals:
dB = 10 log (P1/P2)
Signal amplitude can also be expressed in dB. Since power is
proportional to the square of a signal's amplitude (e.g., a power ratio of 100 is equivalent to an
amplitude ratio of 10), dB is expressed as follows:
dB = 20 log (A1/A2)
Logarithms are useful as the unit of measurement because (1)
signal power tends to span several orders of magnitude and
(2) signal attenuation losses and gains can be expressed in terms of subtraction and addition.
For example, suppose that a signal passes through two channel
segments is first attenuated in the ratio of 20 to 1 on the first leg and 7 to 1 on the second. The total
signal degradation is in the ratio of 140 to 1. Expressed in dB, this becomes 13.01 (10 log 20) + 8.45
(10 log 7) = 21.46 dB.
The following table helps to indicate the order of magnitude
associated with dB:
1 dB attenuation means that 0.79 of the input power survives
3 dB attenuation means that 0.50 of the input power survives
10 dB attenuation means that 0.1 of the input power survives
20 dB attenuation means that 0.01 of the input power survives
30 dB attenuation means that 0.001 of the input power survives
40 dB attenuation means that 0.0001 of the input power survives
Randy H. Katz, randy@cs.Berkeley.edu, Last Updated: 29
December 95
