Wavetable synthesis
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Wavetable synthesis is used in digital musical instruments (synthesizers) to produce natural tone-like sounds. The sound of a existing instrument (a single note) is sampled and parsed into a sequence of wavetables having one period or cycle in each wavetable. Upon playback, these wavetables are used for sample "lookup" in the same manner as in a Numerically-controlled oscillator (or a Digitally controlled oscillator) but 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.
Different wavetables are used for the attack phase (at the beginning of the sound, as the volume increases) and release phase (at the end of the sound, as the volume decreases) of the sound. These are normally very difficult to synthesize with other synthesis techniques, but because these are stored as samples very realistic sounds can be produced with little processing power. The Roland Corporation's series of "Linear Additive" synthesizers such as the D-50 made use of a combination of digitally sampled attack phases.
Because single samples are somewhat limited for synthesis of new sounds, modern wavetable synthesizers can combine multiple samples or even change the sound with filters.
Because of the low processing power required early synthesizers imitated filters and other expensive synthesis methods by rapidly playing successive wavetables in sequence. If each waveform is a little duller (or brighter) than the previous, a filter effect can be imitated.
Special effects can be achieved by selecting a wavetable at random or in a special pattern from the table on a tempo-tick from a sequencer. But the effects are quite strong and don't sound very natural. Of course this can be used on purpose to give the sound a special "edge".
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.
A common misdefinition of the term "wavetable synthesis" is that of any one of many sample based playback devices in popular soundcards and sampling keyboards. This marketing usage of the term probably came from the fact that price-constrained soundcards for IBM PC compatible computers started featuring simplistic digital sound recording and playback several years before they offered any specific support for creating music: keeping a library of samples in memory, playing several samples in parallel, adjusting the pitch to produce various notes, filtering and envelope control. Such features could be only emulated by tracker software, using the CPU of the computer and relying on the soundcard for merely outputting the computed result. The term "sample playback" was deemed inadequate, from a marketing perspective, and the term "wavetable synthesis" was appropriated for use for these soundcards and keyboards, though not accurately.
The definition used herein is the most original definition of wavetable synthesis and in Wavetable Synthesis 101, A Fundamental Perspective (http://www.musicdsp.org/files/Wavetable-101.pdf), it is shown that 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).