Image Processing Reference
that a given word size allows determines the quantization. Allowing too few bits causes
an audible artifact in the sound when it is reproduced.
As you increase the word size, it is harder for the human ear to discriminate the indi-
vidual quantization levels. The extra detail enables the digital filtering algorithms to com-
pute wave shapes more accurately and to avoid rounding and clipping errors. This helps
to retain the highest-possible quality.
Dynamic Range, Logarithmic Scales, and Decibels
An 8-bit value has a range of levels from 0 to 255. Doubling the bits available increases this
range to 65536 discrete values. A 24-bit sample has an even larger dynamic range. Having
an increased dynamic range available is also useful for reducing the amount of noise. Even
a silent passage will have some noise from the random movement of electrons in the dig-
ital-to-analog conversion circuits. Increasing the dynamic range by making the word size
bigger provides a higher signal-to-noise ratio.
For many years audio signals have been measured on a logarithmic scale. This goes
back to the days when telephony was a new invention. In order to measure impedance
so that systems could be matched with one another (this is important for optimum per-
formance), a means of measuring power dissipation across a known resistance was
Figure 7-7 shows a logarithmic curve. The X-axis shows equally spaced units. On the
Y-axis, they are nonlinear.
The dissipation of 1 milliwatt (mW) across a resistance of 600 ohms requires a poten-
tial difference (voltage) of 0.775 volts. From this all manner of other calculations are
derived, such as the root mean square (RMS) or peak power of a signal. This formula has
been the bedrock of audio-level measurement. The Greek omega symbol (
) is used to
indicate a value measured in ohms, and you will often see this used in specifications or on
the back of a speaker cabinet.
The logarithmic scale is used to measure attenuation along a telephone cable because
signals are reduced logarithmically according to the length of the wire. The human ear
also responds logarithmically to the sound pressure level (SPL). This is the force that
sound waves exert when they impinge on the ear.
The unit of measure on the logarithmic scale is called the Bel in honor of Alexander
Graham Bell. The logarithm of the ratio between the measured power and a reference
datum results in a very small value. For most practical purposes therefore, the Bel is too
large a unit so the measurements are expressed in tenths of a Bel (or decibels).
The 1 mW across 600
is our reference and is defined to be the 0 dB reference value.
All other values are measured with reference to that datum.
Taking two power values measured in watts, divide one by the other and then com-
pute the base-10 logarithm of the result and multiply that by 10, because the measurement
is in deci-Bels (dB). Here is the formula.
Power Ratio = 10 * log