Wavetable synthesis

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Wavetable synthesis is a technique used in certain digital music synthesizers to produce natural tone-like sounds. The sound of an existing instrument (a single note) is sampled and parsed into a circular sequence of samples or wavetables, each having one period or cycle per wave; a set of wavetables with user specified harmonic content can also be generated mathematically. Upon playback, these wavetables are used to fetch samples (table-lookup) in the same manner as in a Numerically-controlled oscillator to produce a waveform. However, in wavetable synthesis, the output waveform is not normally static and evolves slowly in time as one wavetable is mixed with another, creating a changing waveform. Looping occurs when the wavetable evolution is halted, slowed, or reversed in time.

Wavetable synthesizers imitate dynamic filters and other computationally expensive synthesis steps by rapidly playing successive wavetables (each with a different waveform stored therein) in sequence. If each waveform is a little duller (or brighter) than the previous, a moving filter effect can be imitated. As noted below, this creates an effect that is equivalent to additive synthesis, with the assumption that all partials in the additive engine are harmonic (integer multiples of the fundamental frequency), and is also related to frequency modulation synthesis; using wavetables, however, significantly reduces the amount of hardware needed, since the sum of partials at each step of each partial's envelope (the part requiring the most compute power) has already been calculated, and all the CPU needs to do is interpolate between them. By contrast, a pure analog additive or FM synthesizer would need several discrete oscillators, envelope generators and volume controls per voice, and a digital version would require a very fast CPU (something that wasn't available when the technology was first being developed), or special (and much more complex) hardware to do the math. For example, the Yamaha DX7 has 6 operators per voice, and 16 voice polyphony, so a total of 96 separate oscillator, EG, and VCA modules would be needed to build an equivalent modular synthesizer. This setup would take several equipment racks to hold. It would also only be useful as an additive synthesizer, since FM requires highly stable oscillators to work properly. (The DX7 actually uses phase modulation -- a sine-wave DCO behind a programmable digital delay line -- combined with two intermediate registers and a fast time division multiplexing system to compute each operator, thus reducing the number of DCOs needed per voice to 1.)

This method differs from simple sample playback in that the output waveform is always generated in real time as the CPU processes the wave sequences, and the waves in the tables are rarely more than 1 or 2 periods in length. The name "wavetable" as applied to soundcards and sample-playback synthesizers is a misnomer; see below for an in-depth discussion.

Some later variations on the technique are Roland's "Linear Arithmetic" synthesizers such as Roland D-50 and Roland MT-32/LAPC-I, which combined complex sampled attack phases with less complex sustain/decay phases (basically a wavetable synthesizer with a 2-entry wave sequence table), and vector synthesis, used in the Sequential Circuits Prophet-VS and Korg Wavestation, which can move through wavetables and sequences arranged on a 2-dimensional grid.

[edit] Palm's wavetable systems

The German synthesizer designer Wolfgang Palm began experimenting with wavetable synthesis in the late 1970s, with his research realized in PPG's line of synthesizers such as the Wavecomputer, Waveterm, and Wave. Palm's implementation of wavetable synthesis employed an array containing 64 pointers to individual (symmetrical) single-cycle waves stored within the instrument. Usually, only a few pointers to these waves were actually used, spread throughout the breadth of the wavetable. The distinguishing feature of the PPG Wave series was that it would interpolate the remaining waves in between the defined pointers, so that changing the position within the table would result in a smooth, unique "morphing" effect between the waves. It should be stressed that Palm's wavetable scheme's strength was in its generation of harsh digital sounds and bell-like timbres, not the emulation of acoustic instruments. It was possible to sample a complex sound into a wavetable by way of the Waveterm device, but the results were invariably artificial, and usually not as interesting as the powerful and bizarre sounds resulting from competent exploitation of the synthesizer's capabilities.

After the demise of the PPG company, Waldorf Music adapted Palm's wavetable oscillator design into their wildly successful Microwave synthesizer module (1988). This design was extrapolated into the Waldorf Wave in the early 1990s, a very large and expensive instrument offering facilities for resynthesis and user-friendly wave and wavetable construction. An all-digital revision of the Microwave soon followed, with a complete line of wavetable synthesizers remaining in production until 2003. Aside from a few improvements designed to eliminate audible aliasing and quantization (signal processing) errors, this wavetable oscillator scheme had not significantly changed since the first days of the PPG wave series.

[edit] Confusion with sample-based synthesis

Palm's systems used wavetable to mean the list of waveforms being processed as part of a patch or program; in more general technical use, however wavetable means the sample data used to generate a sound. This was noticed in the early 1990s by several makers of PC soundcards; starting around 1993, with the introduction of Creative Labs' Sound Blaster AWE-32 and Gravis's Ultrasound cards, the term "wavetable" started to be applied to any card that had a better General MIDI subsystem than the then-common OPL2 and OPL3 FM synthesizers. These subsystems were generally based on low-end sampler ICs, often with no support for per-voice modulation controls or custom patches, limiting their usefulness for music composition greatly. This usage of the term has been downplayed in recent years with the drop in popularity of General MIDI-based music in games, in favor of custom sound engines (which typically call for a more modern DSP-based sound card) and pre-recorded music.

The AWE32 and the Ultrasound are somewhat more powerful than their specification sheets say; the AWE32 in particular was based on the E-mu Emulator III and had uploadable samples (with up to 28 MiB of sample memory), per-voice LFOs and resonant filters, and it also exposed the current sample memory address for each DCO, making it possible to force the DCO to another address on demand. All of these can be used to generate wavetable-style effects, though it should be stressed that the AWE32 is not a wavetable system in the classical sense. The AWE32 also has an OPL3 FM synthesizer that can be used alongside the sampler.

The description of wavetable synthesis in previous sections is the most original definition 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 at frequencies that are an integer multiple of a fundamental frequency of the tone).