Matters Concerning Audio - A Practical Guide to Video and Audio Compression - page 156

Logarithmic
scale

Linear increments

Figure 7-7 Logarithmic scale.

The value measured in dB is a ratio and therefore it only has meaning when
described with respect to a reference value. Taking our 1 mW reference, any values for sig-
nal levels relative to that would be measured in dBmW, which is shortened to dB(m).
The formula for power ratios applies to power measurements in watts. Audio mon-
itoring also measures voltage. Virtually the same formula is used but the result must be
squared. Squaring a value that is converted to a logarithm is accomplished by doubling
the result. Here is the formula for expressing voltage ratios in dB.

()

Voltage1
Voltage2

Voltage Ratio = 20 * log

Computing the dynamic range of the signal for a given sample word size is accom-
plished by adapting the voltage ratio formula like this:

( )

2 word-size

Dynamic range = 20 * log

So for different word sizes in our sampling scheme a table of dynamic ranges can be
computed as shown in Table 7-1.
So, the dynamic range describes the difference between the quietest sound and the
loudest sound that is accommodated within the range of possible values.