Appendix

1 Decibel Mathematics

The standard for representing power ratios is the bel (B). If we increase an initial power value by a factor of 10, we say that it has increased by 1 bel. If we increase the power by a factor of 100 (= 10 · 10, or 102), we say that it has increased by 2 bels. Increasing the power by a factor of 1,000 (= 10 · 10 · 10, or 103) would be an increase of 3 bels, and so forth.

As you can see, even with small increases in bels, the power ratios quickly become very large. For example, increasing by 6 bels is the same as increasing by a factor of 1 million! To avoid having to work in fractions of bels, we use the more common decibel (dB) system. 10 decibels equals 1 bel.

1 dB also conveniently corresponds to roughly the ...

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