The last post noted that the two most popular synthesizer filters are the 2-pole state variable, and the 4-pole “Moog style”. And we started with the state variable—simple, popular, and delivering multiple filter outputs (lowpass, bandpass…) simultaneously. Here, we’ll follow up with comments on the filter associated with Moog (and especially the Minimoog). In general, we’ll refer to this as a 4-pole synth filter.
While this filter is usually thought of as a lowpass filter, the other popular filter types can be derived easily. Many people first saw this in the Oberheim Xpander (and Matrix-12) synths of the ’80s, the idea came from Bernie Hutchins’ Electronotes in the ’70s. So don’t feel that you must go the direction of the state variable is you want multiple filter types, including 2-pole response.
Lowpass response is the overwhelming choice for typical synth use. Note that a 4-pole lowpass is not necessarily better then a 2-pole (as in the state variable)—they are just choices. You might want a 4-pole for the darker Minimoog bass sounds, and a 2-pole for the brassy OB8-style sounds.
The 4-pole is implemented by a string of four one-pole lowpass filter in series. We need corner peaking and resonance control for a synth filter, and we get that by feeding back the output to the input. While trivial in the analog domain, this feedback is the tricky part in the digital recreations. The reason is that it’s not a continuous system, and the obvious way to handle it is to put a delay in that part, so the output of the current sample period is available as input for the next. But this creates some bad side effects, particularly for tuning. In the past, people dealt with this by accounting for those errors.
But it’s not just tuning errors—if it were, that would be simple to fix. The Minimoog popularity, in part, is that it is designed to easily overdrive the filter, to get a “fat” tone. This is another thing that is simple in the analog domain, but doing the same in the digital domain produces noticeably digital artifacts. And if your goal is to make something that sound analog, this is a source of spectacular “fail”.
So instead of this simple delay approach in the 4-pole feedback path, modern ideas use more complex techniques to avoid the large-scale errors in an effort to get closer to how the analog counterpart works. And part of the effort is in dealing with an overdriven feedback path. The result reduced digital artifacts, makes the filter’s behavior more closely resemble its analog counterpart when overdriven, and also gives a smoother, more predictable and more musical sound at high resonance.
Note that these techniques are often called “zero feedback delay” (ZDF) filters. That is meant to highlight the fact a trivial delay is not used. I’m not a huge fan of that, since it’s not meaningful to someone who doesn’t know of the delay it refers to, and of course there are always sources of internal delay in an such filter design. But I mention ZDF so that if you’ve heard it before, be assured that we are talking about those sort of techniques here.
A great resource for this topic is Vadim Zavalishin’s The Art of VA Filter Design (“VA” for “Virtual Analog”).