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. Generating harmonic content 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. Simulating a resonant filter 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: (a) The base frequency counter, wrapping around every period. (b) The resonance frequency counter