Wavetable synthesis

Wavetable synthesis is 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 published in 1979, and has since been used as the primary synthesis method in synthesizers built by PPG and Waldorf Music and as an auxiliary synthesis method for instance by Sequential Circuits, Ensoniq, Access and Dave Smith Instruments.

Principle

Wavetable synthesis is fundamentally based on periodic reproduction of an arbitrary, single-cycle waveform. The distinction to other synthesis methods employing single-cycle waveforms is twofold: 1) multiple single-cycle waveforms are used while 2) one or several wave modulators control the change between those multiple waveforms or mixtures thereof. The wave modulation rate is usually significantly smaller than the sampling rate.

The particular sound associated with wavetable synthesis is unique, since only perfect harmonics are produced. Depending on the details of the actual implementation the sound also contains recognizable artefacts, especially aliasing, quantization and phase truncation noise.

Comparison with other digital synthesis techniques

Wavetable synthesis is closely related to additive synthesis, however unlike additive synthesis the user does not have to work with single harmonics, since each waveform in a wavetable represents a combination of multiple harmonics.

• Sample-based synthesis uses multiple-cycle waveforms and intricate algorithms for pitch-shifting.
• LA synthesis uses short PCM samples for the attack portion of the sound and looped samples (most of them single-cycle loops) for the sustain/release portion of the sound.
• Granular Synthesis uses many overlapping windowed samples. While these samples are very short, they are never periodic.

Confusion with table-lookup oscillators

Practical realizations of this principle often employ digital memory to store samples of the single-cycle waveform. An early non-realtime software implementation, originally called table-lookup oscillator, appeared in MUSIC IV-B. Over time this type of short-memory based oscillator has also become known as wavetable oscillator, which must not be confused with wavetable synthesis as decribed above. Again, in wavetable synthesis multiple such waveforms are in use, originally as a table of 64 waveforms with 128 samples each, while the term "wavetable" for this arrangement appeared later in the PPG literature for the PPG Wave. Both variable and (more commonly) fixed sample rate systems can be used.

The term "wavetable oscillator" therefore should be avoided unless the distinction between the two conflicting uses are unambigous.

Confusion with sample-based synthesis

Starting around 1993, with the introduction of Creative Labs' Sound Blaster AWE32 and Gravis' Ultrasound cards, the term "wavetable" started to be applied as a marketing term to any sound card that used PCM samples as the basis of sound creation. However, these sound cards did not employ any form of wavetable synthesis, but rather a high-end sampler and subtractive synthesis system based on technology from the E-mu Emulator family.

Wavetable

In the context of wavetable synthesis a wavetable is a collection of single cycle waveforms. Together with the wave modulation it defines the basic sound, which is then often altered by additional post-processing like filtering. The structure of the wavetable, that is the number and length of entries, depends on the actual implementation. The individual waveforms and their placement in the wavetable have to follow the musical intent as well as the modulation capabilities of the synthesis engine. The creation of new wavetables is therefore a difficult process unless supported by specialized editing facilities and (near) real-time playback of edited wavetables on the synthesizer. Such editors often require the use of extra hardware devices like the PPG Waveterm or are only present in expensive models like the Waldorf WAVE. More commonly pre-computed wavetables can be added via memory cards or sent to the synthesizer via MIDI. Today wavetables can be created more easily by software and auditioned directly on the computer. Since all waveforms are periodic, the time-domain and frequency-domain representation are exact equivalents of each other and both can be used simulaneaously to define waveforms and wavetables.

Wavetable Types

Several types of wavetables can be identified by the way they are used or created.

1. Transient wavetables capture the evolution of harmonics in a sound over time. They are typically modulated with a ramp or envelope generator, sometimes (also) with an LFO. Creation of such wavetables can be done by employing the STFT on a sample with known and constant pitch.
2. Formant wavetables capture the harmonic changes of sounds played at different pitches through a resonator with fixed resonances. This is most often used for voice-like sounds and requires the wave modulation to follow the playback pitch (often called "keytrack"). Creation of such wavetables requires multiple samples, each with a different pitch.
3. Wave Sequence wavetables often have sudden changes in harmonic content and are typically modulated with one or more LFO to provide rhythmic or loop-like sound effects. They are usually created by a process similar to transient wavetables or by an ad-hoc combination of unrelated waveforms or wavetable segments.
4. Speech wavetables are a specialized wave sequences and mainly modulated with ramp segments. Creation is usually done with the help of Text-to-Speech synthesis software.

All types of wavetables can be usefully combined, although the size of the wavetable and the difficulty to set up the required modulations ultimately limits this process.

Practical Use

During playback, the sound produced can be harmonically changed by moving to another point in the wavetable, usually under the control of an envelope generator or low frequency oscillator but frequently by any number of modulators (matrix modulation). Doing this modifies the harmonic content of the output wave in real time, producing sounds that can imitate acoustic instruments or be totally abstract, which is where this method of sound creation excels. The technique is especially useful for evolving Synth pads, where the sound changes slowly over time.

It is often necessary to 'audition' each position in a wavetable and to scan through it, forwards and backwards, in order to make good use of it, though selecting random wavetables, start positions, end positions and directions of scan can also produce satisfyingly musical results. It is worth noting that most wavetable synthesizers also employ other synthesis methods to further shape the output waveform, for example, Subtractive Synthesis (Filters), Phase Modulation, Frequency Modulation and AM (Ring) Modulation.

References

• Palm, Wolfgang (2009), The PPG Story, Part 4

• Andresen, Uwe (1979), "A New Way in Sound Synthesis", 62nd AES Convention (Brussels, Belgium), Audio Engineering Society (AES) http://www.aes.org/e-lib/browse.cfm?elib=2920 {{citation}}: Missing or empty |title= (help)

• Mauchly, J. William; Charpentier, Albert J. (1987), "Practical Considerations in the Design of Music Systems using VLSI", AES 5th International Conference: Music and Digital Technology, Audio Engineering Society (AES) http://www.aes.org/e-lib/browse.cfm?elib=4672 {{citation}}: Missing or empty |title= (help)

• Bristow-Johnson, Robert (1996), "Wavetable Synthesis 101, A Fundamental Perspective", 101st AES Convention (Los Angeles, California), Audio Engineering Society (AES) http://www.aes.org/e-lib/browse.cfm?elib=7379 {{citation}}: Missing or empty |title= (help) Copy on MusicDSP

• PPG Wave 2.2 Owners Manual (english) (PDF), Palm Productions GmbH