[sdiy] Casio CZ resonant waveforms / Windowed Sync

[Richie Burnett]

Hi Tom,

Neat stuff!

I like your "ghetto demo" board where you can freely alter the saw 
oscillator (modulator) and sine oscillator (carrier) pitches with the pots. 
Very useful for quickly getting a handle on how it sounds, and it sounds 
good!

The way you have it coded at the moment,  (sinusoidal carrier with no DC 
offset,  windowed by the sawtooth modulator)  mimics the sound of a sawtooth 
being passed through a resonant BANDPASS filter.  (You can see this in the 
output waveform  -  It looks like a sawtooth would look like had it been 
passed through a sweepable resonant bandpass filter.  The low-frequency 
downward slope of the sawtooth waveform itself isn't visible in the output, 
only the resonant ringing.)

You can actually mimic different resonant filter responses by slight 
modifications to the carrier waveform before you multiply it with the 
modulator...

A sinusoidal carrier with no DC offset like this  [sin(w)]  before windowing 
gives you a band-pass resonant response.
http://www.richieburnett.co.uk/temp/cz-bp-sim.wav

A cosine carrier with no DC offset like this  [cos(w)]  before windowing 
gives you a high-pass resonant response.
http://www.richieburnett.co.uk/temp/cz-hp-sim.wav

A raised cosine carrier with DC offset like this  [0.5-0.5cos(w)]  before 
windowing gives you a low-pass resonant response.
http://www.richieburnett.co.uk/temp/cz-lp-sim.wav

A raised sine carrier with DC offset like this  [0.5+0.5sin(w)]  before 
windowing gives you a peaking resonant response.
http://www.richieburnett.co.uk/temp/cz-pk-sim.wav

It's also possible to simulate resonance on other waveforms, eg. PWM.
http://www.richieburnett.co.uk/temp/pwm-lp-sim.wav

The nature of the resonance that this CZ algorithm imparts is quite 
interesting because it does not behave like a constant-Q filter.  As you 
sweep it, it does not boost all frequencies by the same amount of dB's.  It 
is highly resonant at high frequencies and runs out of steam if you like at 
low frequencies.  I find this interesting because many real world analogue 
filters that are held in high regard like the TB-303 also display similar 
characteristics.

Fascinating stuff indeed.  All the best techniques are in the old kit it 
seems!

-Richie Burnett,