The Phase distortion synthesis method was first introduced by Casio in 1984 in their CZ range of synths. It’s similar to Frequency modulation synthesis in that they are both built on phase modulation. This type of synthesis refers to when a sine wave is played but is bent out of shape as a result of modifying the phase angle.
Figure A below illustrates how a sine wave gradually transforms into a saw wave as the readout phase angle gets increasingly more distorted. Depending on whether a frequency counter x is either above or below the current distortion point, one of the following 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 like Figure A except that it instead shows how a square wave is developed. For x values below the first knee in the phase angle insert, the y values will rapidly vary between -3.14 and 0. This results in the initial sharp rise of the square. The values found between the first knee and the center knee all equal 0.0. This results in the square having a flat ceiling in the first half wave. Then there is another sudden rise in the phase angle to 3.14. This results in the square wave falling down to its flat floor of -1.0. It stays there until the frequency counter wraps around and the process is repeated. Other phase distortion patterns are supported on the CZ range, including impulse, double impulse, and half-sine. The CZ synths are also capable of creating synchronized and windowed sine waves that emulate resonant filter sweeps.
Phase distortion synthesis works internally by reading a sine wave table that is found in its memory. The most important parts of an initial linear frequency counter are transformed under envelope control into a secondary phase angle signal. This signal is then used to read the sine wave. Depending on the wiring, a wide range of waveshapes can be created.
The phase transforms are made from piecewise linear functions under binary logic control. These transforms show typical sharp knees (and some even show sudden jumps) as they go from minimum to maximum. When it reaches the maximum, the frequency counters accumulator wraps around and starts over. The sharp knees are not very noticeable in the resulting signal as they are smoothed out by the roundness of the modulated sine wave.
Simulating a resonant filter
Figure 19 from the 1985 CZ-series patent illustrates how to reproduce the variable resonance found in analogue voltage controlled filters:
- (a) The base frequency counter should wrap around every period.
- (b) The resonance frequency counter should be at a slightly higher frequency. It will be reset (or “synced”) when the base counter wraps around.
- (c) The resonance frequency counter will be used as a sine wave readout. Note that there will be a significant jump at the reset.
- (d) The inverted base frequency counter.
- (e) Multiply c by d. This levels out the sudden jump in c.
Casio used this method of phase distortion synthesis to create the five different Casio CZ synthesizers.
The VZ-1’s “Interactive phase distortion” synthesis method includes an improved version of phase distortion along with Frequency modulation synthesis.