Phase distortion synthesis
Phase distortion 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 Music 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 introduced the term "phase distortion" for their variety of synthesis.
Casio's implementation of PD utilised a single modulating and carrier waveform; however, as the modulators were composite, many harmonics were created in the resultant waveform, and their amplitudes tended to create linear spectra. This is different from Yamaha's initial approach to phase modulation, where only sine waves (single harmonics) could be used as carrier or modulator, and the resulting spectra were shaped by Bessel functions. Yamaha in later machines allowed the use of non-sine waveforms, enabling generation of more/different overtones through phase modulation.
On the Casio machines the waveforms available for use were rich in harmonics such as a square wave. Other waveforms that are supported on the CZ range are impulse, half-sine and double impulse. The CZ synthesizers also generate synchronised and windowed sine waves in order to emulate resonant filter sweeps.
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 smoothened out by the roundness of the modulated sine wave and not too noticeable in the resulting signal.
Simulating a resonant filter
Figure 19 from the 1985 CZ-series patent shows how to emulate the variable resonance found in analogue voltage-controlled filters:
- (a) The base frequency counter, wrapping around every period.
- (b) The resonance frequency counter at a slightly higher frequency, being reset (or "synced") when the base counter wraps around.
- (c) The resonance frequency counter used as a sine wave readout. Note the nasty sudden jump at the reset!
- (d) The inverted base frequency counter.
- (e) Multiplying c by d. The sudden jump in c is now leveled out.
To summarize in other terms, the filter implementation is a form of digital hard sync, but adds a triangular descending volume envelope running within the sync period. Because the volume always ends at zero, the discontinuities that would cause aliasing in native digital hard sync are avoided. Filter sweep effects are generated in the same way that hard sync effects are generated: by modulating the frequency of the resonance waveform, the timbre changes, adding and subtracting harmonics as desired.
Casio made five different synthesizers using this method of phase distortion synthesis.
The VZ-1 and co's synthesis method ("Interactive phase distortion") is much more similar to phase modulation, rather than being a direct evolution of phase distortion; see next.
Comparison to other types of synthesis
Phase distortion broadly applies similar mathematical concepts to phase modulation synthesis (often euphemised as, and mathematically similar to, frequency modulation), although the implementation and results are not equivalent. Whereas PM - pioneered by John Chowning and commercially debuted in the Yamaha DX7 - uses an oscillating modulator that can have a distinct period, PD applies an angular modulator composed of straight-line segments hard-synchronised to the same period as its corresponding carrier, i.e. modulating each cycle identically. Thus, PM/FM produces Bessel function-derived spectra unless linearised by the application of feedback, whereas PD produces linear spectra. This manifests in PD synths' reputation for being easier to produce traditional subtractive sounds, such as those typically associated with analogue synths, which are characterised by linear spectra. These facts demonstrate how although the broad concept - alteration of phase - is the same, implementation and results differ greatly.
Casio's own later engine named Interactive Phase Distortion (iPD), which featured in their VZ synths (VZ-1, VZ-10M, and VZ-8M; the first two also rebadged by Hohner as the HS-2 resp. HS-2/E), actually bears very little resemblance to 'actual' PD, being based around an idiosyncratic type of PM instead. In iPD, multiple oscillators are combined in various configurable routings (similar to Yamaha's "algorithms") and can modulate each other using PM or ring modulation (the latter not available in Yamaha's system). However, unlike in Yamaha's implementations, direct PM is restricted to a carrier:modulator ratio of 1:2 - with other ratios requiring workarounds and often making some oscillators contribute little or nothing to the desired sound. iPD has some added features that give it advantages in some contexts, but it is generally not as versatile as Yamaha's method for 'pure' phase modulation.