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Main Group 33: Amplitude Modulation
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Sub Id  Contents

01      Basic Ring Modulation with Multiplier
    1   general purpose
    2   sinus and block wave

10      Ring Modulation of External Soundfiles
    1   speech1.SF
    2   santur1.SF

50      "Classical" Amplitude Modulation
    1   general purpose

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Overview

In this main group, we can only represent two out of three main
techniques of amplitude modulation: ring modulation and
"classical" amplitude modulation. Csound does not have any
provisions (unit generator) for single-sideband modulation. 

In "classical" amplitude modulation, the amplitude of the
modulator is best expressed as a function of the modulation index
'imod' and the amplitude of the unmodulated carrier oscillator. 

For example, let the signals be two sinusoids.

'Imod=0': the amplitude of the modulator is zero and there is no
modulation. The spectrum gives the carrier.

'Imod=1': 100% modulation, amplitude of the modulator equals the
amplitude of the carrier. Output contains the carrier frequency
'ifqc' at the original amplitude, and two sidebands at ifqc+ifqm
and ifqc-ifqm, both with a half of the original amplitude. 

Ring modulated signals are obtained by multiplying two signals or
by applying a wave to the amplitude input of a signal generating
oscillator. In both designs, the original spectrum of the
modulating wave is split in two (or more) identical images above
and below the carrier frequency(ies). The main difference with
classical AM is that the carrier frequencies do not appear in the
output. (Dodge 1985: p.80-85)

Both techniques require careful treatment of amplitude values:
the multiplication of two amplitudes can easily lead to
out-of-range amplitudes. 

Negative frequencies are reflected into the positive frequency
domain. 

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Suggested Reading

Dashow, James 1978.
"Three Methods for the Digital Synthesis of Chordal Structures
with Non-Harmonic Partials."   
Interface 7, pp. 69-94.

Moore, F.R. 1990.
"Amplitude Modulation."
Elements of Computer Music.
Prentice-Hall, pp. 185-187.
 
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33_01_1
additional parameters: ifc, ifqm, ifm


The multiplier of this design functions as a general purpose ring
modulator. The amplitude of the modulating unit is 1. 
In ring modulation it is safe to keep one signal close to unity,
in order to limit the audio samples to the permitted amplitude
range of +- 32000. 


Three sample notes are played. 

1) carrier 800 Hz, modulator 50 Hz: 
      output 750, 850 Hz

2) carrier 800 Hz, modulator 111, 222, 333 Hz:
      output: 467, 578, 689 Hz

3) carrier 800, 1600, 2400 Hz, modulator 107 Hz:
      output: 693, 807, 1493, 1707, 2293, 2507 Hz 

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33_01_2
additional parameters: 


This instrument attempts to prolong harmony into timbre: a chord,
played by ring modulation instrument i1 is followed by a
gong-like tone, whose components are the fundamentals of the
chord.

The latter sound is perceived as one, yet its tone quality is
related to the chord's harmony. Here is the passage:

(score)


Instrument 1 produces the ring modulation chord, by combining a
sinus with a block wave.  The dominant frequencies are the
differences between ifqc and ifqm: -576 +1424 / -273 +1727 / -458
+3542 / -864 +3136 / -658 +3342  Hz.  These are the fundamentals
of the modulated block wave.

The envelope controlling the sinus wave is also controlling the
general envelope of the note and the spectral evolution. At first
the attack and duration are short (A), then the attack switches
to a cresc-decresc type with a medium duration (B). Finally, the
frequencies are repeated (273, 455, 576, 648, 864 Hz) as
components of a gong timbre with short attack and long duration
(C). 

Instrument 2 is equal to 02_01_3. An additive synthesis tone
through overlapping score calls. (Risset 1969: #550; Vercoe 1993:
morefiles/risset4.orc)

(flowchart)
(.orc and .sco files)

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33_10_1
additional parameters: ifm, istsec


33_10_2
additional parameters: ifm, istsec


In these designs, exterior soundfiles are read in with the
SOUNDIN unit generator and ring modulated by a second signal,
i.c. a sinus. The amplitude of the incoming signal is normalized
by the BALANCE unit generator.

The parameter istsec specifies the exact time at which SOUNDIN
starts reading from the given audio file into the internal array
a1.

(flowchart)
(.orc and .sco files)

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33_50_1
additional parameters: ifc, imod, ifqm, ifm


This is a 'classical' amplitude modulation design through which
one can control the precise percentage of amplitude modulation of
a signal.
 
The first section plays notes with an amplitude modulation
increasing from 0 to 1 in steps of 0.2 imod. The amplitude
modulation is applied to two sinus signals, but this is
extendable to the wide range of complex carriers and modulators. 

The amplitude is kept to the same output level in function of a
chosen imod factor. In other words: for whatever amount of
modulation, the amplitude will equal the specified
value iamp.

In the second section imod stays at 100% modulation. The effect
of a changing modulator frequency is tested by varying ifqm from
150 Hz to 1200 Hz. It should be noted that in the latter case,
the output also contains the reflected "negative" frequencies.

Suggestions:
Create an electronic "tremolo" with a small 'imod' and subaudio
ifqm. For imod=1, subaudio ifqm leads to a strongly pulsating
tone. As this concerns LFO modulation of amplitude, within the
ACCCI an electronic tremolo instrument belongs to main group 01
and not to main group 33.

(flowchart)
(.orc and .sco files)
