Owner`s manual

24
CHAPTER 3 -
The Craft of audio Synthesis
CHAPTER 3 -
3.6.5.1
Sidebands and Sideband Spectra
What happens to the spectrum of a sine wave when we modulate its amplitude? What
happens when we modulate its frequency?
Clearly, since the signal that results from AM or FM methods is no longer a plain vanilla
sine wave, then, in the frequency domain, it must have some additional components.
These additional components are called
sidebands.
They have been studied for at least a
century, and are pretty well understood physically and mathematically.
Audio synthesis is probably the only application of AM or FM modulation where we
are interested in sidebands for their own sake, as something to listen to directly; in the
past, this stuff was only interesting to radio engineers, radar, sonar, television broadcast
engineering. In those disciplines, modulation sidebands are products of broadcasting
methods, in the electromagnetic spectrum. Because of that historical background, some
of the conventional language for talking about modulation processes is a little weird:
the signal being modulated is often referred to as the
carrier signal
, and the signal that
carrier signal, and the signal that carrier signal
provides the modulation pattern is called the
program.
(Guess why.)
Any form of modulation generates, for each component of the
original signal, at least one
lower sideband
– at a frequency equal
lower sideband – at a frequency equal lower sideband
to the component minus the modulating frequency – and at least
one
upper sideband,
at a frequency equal to the component plus
the modulating frequency. If the carrier – the original signal - is
itself complex, with multiple spectral components, then each of
its components will produce its own sidebands independently of
all the others. Likewise, if the modulating signal – the program
- is complex, the arithmetic applies separately to each of its
components.
So, just for example, if you modulate a 10-component carrier signal
with a 10-component program signal, the signal resulting from the
modulation will have not less than 100 spectral components. This
can get very messy; the most useful thing you can do with such a
signal, before you do anything else, is  lter it to get rid of some of
the fuzz.
3.6.5.2
Amplitude Modulation
Suppose we modulate the amplitude of a 1000Hz sine wave with a 5Hz sine wave. The
result is indistinguishable from what we would get if we mixed three sine waves, at
995Hz, 1KHz, and 1005Hz. They are the same signal.
The 995Hz component of the output is the lower sideband resulting from the modulation,
and the 1005Hz component is the upper sideband.
Given this for a carrier:
. . . and this for a program
here's the AM result:
carrier
spectrum
program
spectrum
upper
sideband
lower
sideband
carrier
weakend
the carrier
is gone
and varyin
g
amplitude
depending
on the
modulation
depth
?
variable
number of
sidebands
here's the ring modulation:
and here's the FM result: