Main Group 33: Amplitude Modulation

Overview

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.

Suggested Reading

Moore, F.R. 1990.
"Amplitude Modulation."
Elements of Computer Music.
Prentice-Hall, pp. 185-187.

33_01_1

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

Orchestra and Score

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33_01_2

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:

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)

Orchestra and Score

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33_10_1

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.

Orchestra and Score

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33_10_2

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.

Orchestra and Score

WAV and mp3

33_50_1

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.

Orchestra and Score

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