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Additive Synthesis

One of the very first computer music techniques introduced was additive synthesis [382]. It is based on Fourier's theorem which states that any sound can be constructed from elementary sinusoids, such as are approximately produced by carefully struck tuning forks. Additive synthesis attempts to apply this theorem to the synthesis of sound by employing large banks of sinusoidal oscillators, each having independent amplitude and frequency controls. Many analysis methods, e.g., the phase vocoder, have been developed to support additive synthesis. A summary is given in [428].

While additive synthesis is very powerful and general, it has been held back from widespread usage due to its computational expense. For example, on a single DSP56001 digital signal-processing chip, clocked at 33 MHz, only about $ 60$ sinusoidal partials can be synthesized in real time using non-interpolated, table-lookup oscillators. Interpolated table-lookup oscillators are much more expensive, and when all the bells and whistles are added, and system overhead is accounted for, only around $ 12$ fully general, high-quality partials are sustainable at $ 44.1$ KHz on a $ 33 MHz$ DSP56001 (based on analysis of implementations provided by the NeXT Music Kit).

At CD-quality sampling rates, the note A1 on the piano requires $ 22050/55\approx 400$ sinusoidal partials, and at least the low-frequency partials should use interpolated lookups. Assuming a worst-case average of $ 100$ partials per voice, providing 32-voice polyphony requires $ 3200$ partials, or around $ 64$ DSP chips, assuming we can pack an average of $ 50$ partials into each DSP. A more reasonable complement of $ 8$ DSP chips would provide only $ 4$ -voice polyphony which is simply not enough for a piano synthesis. However, since DSP chips are getting faster and cheaper, DSP-based additive synthesis looks viable in the future.

The cost of additive synthesis can be greatly reduced by making special purpose VLSI optimized for sinusoidal synthesis. In a VLSI environment, major bottlenecks are wavetables and multiplications. Even if a single sinusoidal wavetable is shared, it must be accessed sequentially, inhibiting parallelism. The wavetable can be eliminated entirely if recursive algorithms are used to synthesize sinusoids directly.


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA