Editing Phase distortion synthesis (section)

== 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 [[Window function|windowed]] at the fundamental frequency. Frequencies could be controlled but not resonance amount. [[Image:Casio.CZ101.resonance.png|thumb|300px|right|Figure 19 from the USPTO CZ-series patent application depicting how to eliminate the sudden jumps in the variable resonance circuitry (here showing the second [[harmonic]] coming into view.)]]

Figure 19 from the 1985 CZ-series patent shows how to emulate the variable resonance found in analogue [[voltage-controlled filter]]s:
* ('''a''') The base frequency counter, wrapping around every period.
* ('''b''') The resonance frequency counter at a slightly higher frequency, being reset (''or [[Oscillator sync|"synced"]]'') when the base counter wraps around.
* ('''c''') The resonance frequency counter used as a sine wave readout. ''Note the sudden jump at the reset, which causes significant distortion.''
* ('''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 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{{clarify|date=December 2014}}. 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.