Mackie Digital 8 Bus Owner's Manual page 200

Appendix B
Digital 101
If you've been involved in the audio biz for a
while, chances are you have at least some
fundamental knowledge of the physics of sound
and of what digital audio is all about. Numerous
articles, papers, and books have been written on
the subject and doubtless you've read some of
them. If not, check out the list of recommended
books in Appendix K.
Nevertheless, this section is devoted to the
fundamentals of digital audio which, for some,
may be new information and serve its intended
purpose, and for others may serve as a refresher
course, to exercise those brain cells and refresh
your internal RAM memory.
Sound and Signal
Sound waves have two important attributes
used to describe them. One is frequency , which
describes the number of vibrations that occur
per second. The higher the frequency, the
faster the vibration, and the higher the pitch.
The other attribute is amplitude , which de-
scribes the intensity of the vibration. The
higher the amplitude, the louder the sound.
These attributes are conveyed through the
atmosphere in the form of varying air pressure.
A sound wave is composed of a region of high
pressure (compression), followed by a region of
low pressure (rarefaction). A microphone has a
sensitive diaphragm that moves in response to
these sound waves, and converts the mechani-
cal energy of the sound into electrical energy.
The electrical signal that is used to repre-
sent the sound wave is composed of alternating
positive voltages (corresponding to compres-
sions) and negative voltages (corresponding to
rarefactions). The electrical signal is what
we're concerned with here, because that's what
the Digital 8•Bus uses. We'll use a sine wave
in our examples, which represents a perfect
tone at a single frequency (see Figure B-1).
0 V
Figure B-1. Sine Wave
The Binary Number System
You probably know that in the digital world,
the language spoken consists of ones and zeros.
This is the binary number system. We're used
to using the decimal system, which is base 10.
With the decimal system we have ten different
symbols to represent numbers (one for each
finger). When we reach the tenth symbol, we
start a new column which represents how many
10s we've counted. Each column increases by a
factor of 10 over the previous column.
In the binary system, we have only two sym-
bols to represent numbers, so it's base 2. When
we reach the second symbol, we start a new
column which represents how many 2s we've
counted. Because of this, binary numbers look
a lot bigger than decimal numbers. For example,
the number 20 is written 10100 in binary.
So how can a rapidly changing analog elec-
trical signal be represented by a bunch of ones
and zeros?
The Analog-to-Digital Converter
The analog signal must be converted into a
series of binary numbers by an analog-to-digital
converter (ADC). The ADC takes periodic mea-
surements of the analog signal and assigns a
numeric value to represent the level of the sig-
nal at the time it is measured. In this fashion,
the ADC takes "snapshots" of the analog audio
signal, much like a motion picture camera
takes snapshots (frames) of a live scene. When
the still pictures are shown in rapid succes-
sion, it fools the eye into thinking you're seeing
movement, or motion pictures. In the same
way, when the binary numbers are played back
through a digital-to-analog converter (DAC), it
fools the ear into thinking you're hearing con-
tinuous analog sound. This method of sampling
is referred to as pulse code modulation (PCM).
See Figure B-2.
Time
Digital 101
B-1