#
Sample Resolution

Sample resolution (the number of bits per sample) determines how many
gradations of amplitude (corresponding to loudness) can be represented
in the digital waveform. The range of amplitudes from the most
negative possible sample value to the most positive is referred to as
the *dynamic range* and is normally expressed in decibels (dB)
relative to the smallest non-zero digital value (i.e., 1). For
example, with 16-bit resolution, the largest positive value
representable is 32,767 and the smallest value representable is
-32,768 giving a total range of 65,536 values or about 96 dB.
The conversion from linear amplitude values to decibels is defined as
20.0 times the logarithm of the linear value divided by the scale
reference level. In this case, the reference level is 1 so:
```
```

20.0 * log10(65638 / 1) = 96.3

The next figure illustrates the effects of varying sample
resolution. An analog sine wave is sampled at moderate resolution
(circles correspond to about 6 bits resolution) and at very coarse
resolution (asterisks correspond to about 3 bits resolution). While the
higher resolution samples approximate the shape of the waveform fairly
closely, the low resolution samples give a coarse, stair-step,
approximation to the original waveform shape.