Phase Distortion Synthesis

NOTE: any readers who are struggling to understand this text, here are links to the missing Figures A and B: Figure A Figure B

Phase distortion synthesis is a synthesis method introduced in 1984 by Casio in its CZ range of synthesizers, and similar to phase modulation synthesis in the sense that both methods dynamically change the harmonic content of a carrier waveform by application of another waveform (modulator) in the time domain. Casio introduced the term 'phase distortion'. Yamaha had previously produced the first Phase Modulation synthesizers in their DX series of synthesizers: Yamaha mistakenly promoted their machines as FM when in fact used phase modulation. Both methods produce composite waveforms whose harmonics are the sum and difference of the carrier and modulator waveforms.

Figure A shows how a sine wave gradually turns into a saw wave as the readout phase angle gets more and more distorted. Depending on whether a frequency counter x, is above or below the current distortion point d (the sharp knee in the phase angle insert) one of two equations must be solved:

if(x > d) return sin( x * d / pi); else return sin((x-d) * pi / (1-d) + pi);

Figure B is similar to A, only showing the development of a square wave instead. For x values below the first knee in the phase angle insert, the y values will vary rapidly between -3.14 and 0 resulting in the initial sharp rise of the square. Values between the first knee and the center knee all equals 0.0 resulting in the squares flat ceiling in the first half wave. At this point there is again a sudden rise in the phase angle up to 3.14, resulting in the fall of the square wave down to its flat floor at -1.0 where it stays until the frequency counter wraps around and repeats the process.

Casio's implementation of PD utilised a single modulating and carrier waveform, however, as the waveforms were composite, many harmonics were created in the resultant, output waveform. This is different to Yamaha's approach where only sine waves (single harmonics) could be used as carrier or modulator (either 4 or 6), though Yamaha did change this in later machines and allowed the use of composite waveforms such as saw tooth waves. 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 counters 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.