# Digitized Sound

Nearly everything mentioned in the previous tutorials about sound and
waveforms applies to digitized sounds or digital waveforms as
well. However, because digital waveforms are sampled *approximations* to
continuous functions of time, there are some important differences to
be aware of and there is some new terminology to learn. First, digital
waveforms are described in terms of their sampling rate in
*Hertz* and sample resolution in *bits* per sample. The term
*Hertz*, abbreviated *Hz*, normally means *cycles per
second* when describing waveforms, but it is generalized to
*samples per second* when describing a sampling rate. Each
sample in a digital waveform is a measurement of the amplitude of an
analog waveform at an instant in time. The sampling rate specifies how
many measurements of the analog signal amplitude are made per second
by the Analog to Digital Converter (ADC) hardware of the
computer. Similarly, when digital waveforms are converted to analog
signals (using a Digital to Analog Converter or DAC), sampling rate
refers to how many times per second the (DAC) hardware must be updated
with a new sample value.
Sample resolution
specifies the accuracy of each amplitude measurement made by the ADC
hardware. The more *bits* of resolution, the greater the
accuracy. A *bit* is defined as one binary digit, that is, either
the value 0 or the value 1. Thus, when only one bit is used to represent the
value of an amplitude measurement, the amplitude must be either 0 or
1. If two bits are used to represent amplitude values, then four
possible amplitude values can be represented (0, 1, 2, and 3). More
generally, the number of amplitude values that can be reresented by a
given number of bits is 2**N where N is the number of bits. Using a
large number of bits per sample allows the full amplitude range of an
ADC to be partitioned into a large number of very small steps.

In the following figure, the X axis is time in msec and the Y axis
is amplitude in arbitrary units. This figure shows an analog sine wave (solid line)
is sampled (illustrated by the circle symbols) at a comparatively high
rate compared to its frequency and with good sample resolution.