Digital Sound & Music: Concepts, Applications, & Science, Chapter 5, last updated 6/25/2013
audio signal that is related to the true signal. If you subtract the stair-step wave from the true
sine wave in Figure 5.8, you get the green part of the graphs in Figure 5.9. This is precisely the
error i.e., the distortion resulting from quantization. Notice that the error follows a regular
pattern that changes in tandem with the original “correct” sound wave. This makes the distortion
sound more noticeable in human perception, as opposed to completely random noise. The error
wave constitutes sound itself. If you take the sample values that create the error wave graph in
Figure 5.9, you can actually play them as sound. You can compare and listen to the effects of
various bit depths and the resulting quantization error in the Max Demo “Bit Depth” linked to
this section.
(a) (b)
Figure 5.9 Error wave resulting from quantization
For those who prefer to distinguish between noise and distortion, noise is defined as an
unwanted part of an audible signal arising from environmental interference like background
noise in a room where a recording is being made, or noise from the transmission of an audio
signal along wires. This type of noise is more random than the distortion caused by quantization
error. Section 3 shows you how you can experiment with sampling and quantization in
MATLAB, C++, and Java programming to understand the concepts in more detail. Dynamic Range
Another way to view the implications of bit depth and quantization error is in terms of dynamic
range. The term dynamic range has two main usages with regard to sound. First, an occurrence
of sound that takes place over time has a dynamic range, defined as the range between the
highest and lowest amplitude moments of the sound. This is best illustrated by music. Classical
symphonic music generally has a wide dynamic range. For example, “Beethoven’s Fifth
Symphony” begins with a high amplitude “Bump bump bump baaaaaaaa” and continues with a
low-amplitude string section. The difference between the loud and quiet parts is intentionally
dramatic and is what gives the piece a wide dynamic range. You can see this in the short clip of
the symphony graphed in Figure 5.10. The dynamic range of this clip is the difference between
the magnitude of the largest sample value and the magnitude of the smallest. Notice that you
don’t measure the range across the horizontal access but from the highest-magnitude sample
either above or below the axis to the lowest-magnitude sample on the same side of the axis. A
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