Casio's DCFs seem to be some special beasts. Some sound designers claim
they sound very analog, and, given the fact that they indeed have analog in
and outputs, believe that it is a truly analog filter. An additional point
usually is that the filters have true resonance control  a feature unseen in
commercial synthesizers' digital filters until the late 1980s.
However, looking closer (see pinout below) reveals a clock input which is a
good indication that something timediscrete is going on and we are
definitely not dealing with your average transistor ladder or OTAbased
filter.
A quick patent search reveals several interesting Casio patents on
digital filters dating back to the early 1980s, also digital filters with
resonance control pop up, for instance Patent 4,467,440. What we basically see here is indeed an
IIR (Infinite Impulse Response) filter, although by the way described it
looks like only the control is truly digital while anything else,
i.e. summing, multiplication, and also storing the timediscrete signals is
performed in the analog domain using ordinary adders, multipliers, and
S&H stages.
This would explain why this filter is perceived "analog" and exhibits a
saturation behavior like conventional analog filters, while internally being
digital (i.e. timediscrete) by nature:
Operational amplifiers (as used within analog arithmetic components like
adders and multipliers/amplifiers) expose a certain distortion behavior,
namely the tanh function (hyperbolic tangent). The application of
this function to certain stages within the filter computation is crucial as
this is what gives the Moog (transistor ladder) and OTAbased (e.g. SSM2040)
filters their distinct sound.
(If you're interested in what makes analog filters sound the way they do
and how this can be achieved in software, have a look at Oscillator
and Filter Algorithms for Virtual Analog Synthesis by Vesa
Välimäki and Antti Huovilainen. The same authors also published
some interesting papers on the DAFX
conference series.)
