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Phase distortion (PD) synthesis is a synthesis method introduced in 1984 by Casio in its CZ range of synthesizers. In outline, it is similar to phase modulation synthesis as championed by Yamaha Corporation (under the name of frequency modulation), in the sense that both methods dynamically change the harmonic content of a carrier waveform by influence of another waveform (modulator) in the time domain. However, the application and results of the two methods are quite distinct.
Casio made five different synthesizers using their original concept of PD synthesis (with variations). The later VZ-1 and co's synthesis method Interactive phase distortion is much more similar to the aforementioned phase modulation, rather than a direct evolution of phase distortion; see below.
Casio's implementation of PD used oscillators generated by modulator and carrier waveforms, synchronised to each other per-cycle. The modulators were various angular waves that could 'distort' the carrier's sine into other shapes, to a degree derived from the "DCW" envelope. In doing so, many harmonics were created in the output. As modulators were rich in harmonic content, they could create spectra more linear, i.e. more similar to traditional subtractive spectra, than Yamaha's phase modulation (PM/FM) synthesis. PM does not require oscillator sync but was for a long time limited to sine waves, which meant output spectra bore the non-linear hallmark of Bessel functions. PD is a different type of PM - whose very different modulators caused significant difference in operation and sound between PD and PM. Thus the two aren't directly equivalent.
The phase transforms are all assembled from piecewise linear functions under binary logic control and shows characteristic sharp knees (and for some transforms, even sudden jumps) as they move from minimum to maximum, where the frequency counter's accumulator wraps around and starts over. The sharp knees are smoothed by the roundness of the modulated sine wave and not too noticeable in the resulting signal.
As well as being more capable of generating traditional linear spectra, the CZ synthesizers can also emulate resonant filter sweeps. This was done using sine waves at the resonant frequency, synchronised and windowed at the fundamental frequency. Frequencies could be controlled but not resonance amount.
Figure 19 from the 1985 CZ-series patent shows how to emulate the variable resonance found in analogue voltage-controlled filters:
To summarize in other terms: The resonance is a form of digital hard sync, composed of a sine wave at the resonant frequency, amplitude enveloped by and hard-synced to a window function at the fundamental frequency. The window function can take various shapes, including sawtooth and triangle, thus determining the 'basal' spectrum upon which the resonant effect is superimposed. Since the amplitude of all available window functions ends at zero, this removes sharp discontinuities in the synced sine wave, which is a well-known way to reduce aliasing in digital sync. However, some aliasing is still present due to discontinuities in the function's derivatives. Thus, filter sweep effects are generated the same way as sync effects: by modulating the frequency of the resonance (DCW envelope), the timbre changes, adding and subtracting harmonics to/from the chosen fundamental spectrum around the chosen resonant frequency.
前述の通り、位相歪みは位相変調合成とほぼ同じ数学的概念を適用していますが、その実装と結果は同等ではありません。ジョン・チャウニングが先駆者となり、ヤマハが商業的に採用した位相変調（PM）は、独自の周期を持つことができる発振変調器を使用するのに対し、位相歪み（PD）は、対応する搬送波と同じ周期にハード同期された直線セグメントの角度変調器を使用し、各サイクルを同一に変調します。PM/FMは、フィードバックを適用して線形化しない限り、ベッセル関数由来のスペクトルを生成しますが、PDはより線形なスペクトルを生成します。この違いは、PDシンセサイザーが、アナログシンセサイザーによく見られるような、線形スペクトルを特徴とする伝統的な減算合成サウンドをより簡単に生成できるという評判に表れています。これらの事実は、位相の変化という大まかな概念は同じでも、実装と結果が大きく異なることを示しています。
カシオが後に開発したインタラクティブ・フェーズ・ディストーション（iPD）と呼ばれるエンジンは、同社のVZシンセサイザー（VZ-1、VZ-10M、VZ-8M。最初の2機種はホーナーによってHS-2とHS-2/Eとして再ブランド化もされている）に搭載されたが、実際には「実際の」PDとはほとんど似ておらず、独自のタイプのPMに基づいている。iPDでは、複数のオシレーターがさまざまな設定可能なルーティング（ヤマハの「アルゴリズム」に類似）で組み合わされ、PMまたはリングモジュレーション（後者はヤマハのシステムでは利用できない）を使用して互いにモジュレーションすることができる。オシレーターの組み合わせとルーティングに関するカシオのオプションは、ヤマハよりも柔軟である。たとえば、VZ10-Mは、DX7の32のアルゴリズムと比較して、90の独自のオシレーターとモジュレーションの組み合わせが可能だ。さらに、VZ-10Mの発振器は8種類の波形を備えているため、正弦波のみを使用するDX7よりも複雑な音作りが可能になります。