Wavetable synthesis

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Wavetable synthesis is a technique used in certain digital music synthesizers to implement a restricted form of real-time additive synthesis. The technique was first developed by Wolfgang Palm of PPG in the late 1970s, and has since been used in various forms in other synthesizers built by Sequential Circuits, Ensoniq, Yamaha, Korg and Waldorf Music. The signature sound associated with wavetable synthesis is due to the limitations of the technique and heavily influenced by the widely varying implementation details.

[edit] Theory of operation

The bases of wavetable synthesis are bandlimited periodic waveforms (time-domain implementation) or (mathematically equivalent) finite harmonic spectra (frequency-domain implementation). The evolution of musical timbre over time is approximated by placing different waveforms or spectra in a table and picking the most appropriate one at any time instant during playback.^[1] Since simply switching between two dissimilar waveforms can introduce unpleasant artefacts into the sound, the wavetable has to fulfil certain requirements depending on the implementation details. For instance, the wavetables are often arranged so that the start sample for each waveform is at a positive-going zero-crossing and a switch from one waveform to the other is made only at these zero-crossings. Another refinement is to (additionally)interpolate between two or more different waveforms or spectra to produce smoothly varying timbres and to reduce the storage requirements. By restricting waveforms to the symmetrical, the storage requirements can be halved.

The use of the term wavetable is often inexact. The original usage as introduced by PPG described a collection of waveforms placed successively into memory by interpretation of a wave control table which contained pointers to ROM waves and escape characters to effect interpolation between those ROM waves. In the context of arbitrary waveform generation, direct digital synthesis or numerically-controlled oscillators the term wavetable refers to samples of a single (periodic) waveform. In a frequency-domain implementation the same term may be used to describe the result of rendering a spectrum into the time-domain, or even less accurately, for the components of the spectrum itself.

[edit] Wavetable creation

To imitate the sound of an existing instrument with wavetable synthesis, a single note (with constant pitch) is sampled and processed using a spectrum analyzer, producing a graph of overtones contained in the sample. This graph is then parsed into a sequence of samples or wavetables, each having one period or cycle per table, generated by adding together the partials at each parse point.^[2] A set of wavetables with user-specified harmonic content can also be generated mathematically. Both methods of producing a wavetable are easily combined. The mathematical equivalence of time-domain and frequency-domain representation also makes it possible to freely switch between either during creation of a wavetable.

Editors for wavetables are not normally part of a synthesizer's controls. External hardware devices are needed, like the PPG Waveterm, or software running on a computer. Even then, the creation of wavetables is a process most musicians find difficult; the results are often unsatisfactory for those who have not mastered the intricacies of implementation. Recognizing this, synthesizer manufacturers have produced instruments that provide little or no control over their wavetables.

[edit] Practical Use

During playback, the waveform produced can be changed by switching to a different starting point in the wavetable, usually on command from an envelope generator or low frequency oscillator. Doing this modifies the spectral characteristics of the output wave in real time, producing sounds that can imitate certain analog instruments (such as organs, pianos, harpsichords and reed instruments) acceptably without requiring the use of a pulse code modulation technique, which requires much more memory and higher sample rates for good results. The technique is also useful for evolving Synth pads, where the waveform changes slowly over time and can reverse itself or loop back to an arbitrary point.

The key to creating convincing musical results from a wavetable synthesizer lies in the choice (or creation) of a suitable wavetable and the control of the playback point within that table. It is often necessary to understand how the wavetable was created in order to make correct use of it. Many wavetables contain the attack portion of a sound followed by sustain and release; that is, the temporal evolution of the timbre is encoded into the wavetable. In other instances the wavetable contains different timbres of the same sound to be combined with different pitches during playback; for example, with a synthesized choir, to prevent the formants from shifting with the playback pitch. These two different techniques may even be combined in a single wavetable.

Since a wavetable oscillator can generate arbitrary waveforms, it is also possible to load simple sine wave, square wave and sawtooth wave tables and use the synthesizer like an analogue synthesizer, using subtractive synthesis to modify the sound. Also, some wavetable synthesizers (such as the PPG Wave 2.3 with Waveterm) can reset the loop point on the phase accumulator to a period longer than a single cycle, making a PCM mode possible with minimal hardware changes.

[edit] Comparison with other digital synthesis techniques

Wavetable synthesis has similar capabilities to other synthesizers in the real-time additive synthesis family, as well as to digital frequency modulation synthesis systems such as the Yamaha DX and OPx series; however, wavetable synthesizers require less hardware to produce a usable system. The entire oscillator can be implemented using a few 7400 series TTL ICs and small-capacity static RAM ICs, something that was important in the late 1970s and early 1980s (when memory prices were still relatively high, and high-powered CPUs such as the Motorola 68000 were uncommon and expensive); most other digital synthesizers of the time either implemented each partial separately, making assembly more complex (this is also how most electronic organs are built), or used custom ICs to bring the chip count down.

Later wavetable synthesizers had antialiasing capabilities, where the transitions between waves were mediated by the CPU instead of simply switching the starting address of the loop, as well as subtractive-style filters, since the moving filter effect that a wavetable patch provides is somewhat "harsh" and FM-like without antialiasing, and filters were easier to implement at that time.

[edit] Confusion with sample-based synthesis

Starting around 1993, with the introduction of Creative Labs' Sound Blaster AWE32 and Gravis's Ultrasound cards, the term "wavetable" started to be applied to any sound card that had a better General MIDI subsystem than the then-common OPL2 and OPL3 FM synthesizers. This was based on a misunderstanding between the technical definition of a wavetable (which is the actual sample data used to generate an arbitrary wave), and the PPG usage of the term (which referred specifically to their implementation of wavetable synthesis, as described above). The AWE32 was not an additive synthesizer, but a high-end sampler and subtractive synthesis system based on technology from the E-mu Emulator family.

The description of wavetable synthesis in previous sections is based on the original meaning of the term and (as shown in the reference below) wavetable synthesis is equivalent to additive synthesis in the case that all partials or overtones are harmonic; that is, all overtones are an integer multiple of a fundamental frequency of the tone.

[edit] Notes

[edit] External links

• Wavetable Synthesis 101, A Fundamental Perspective
• Wavetables and samplers
• Orpheus and the New Sample-Loop Synthesis method