yes he ran

The life cycle of performance-critical code is supposed to go in three phases: (1) make it work. (2) make it work right. (3) make it work fast. In truth, there's probably another step, (4) make it work right and fast.

Over the last few days, I've been revisiting some of my plugins and doing a step-two on them, fixing some long-standing bugs. In particular, I've been relying heavily on a particular digital filter implementation that becomes, um, explosively unstable at what are really fairly moderate cutoff frequencies.

In the DSP technical sense, a filter amplifies or suppresses portions of an audio signal based on their frequency. I've been relying heavily on one particular kind of digital filter, the Chamberlin 12dB/octave state variable type. This has the advantage of being really simple to code and very flexible. A single block of code simultaneously calculates the low-pass, high-pass, band-pass, and band-stop outputs from the filter. This is good if, like me, you never know what you're going to want. Low-pass filters are the bread and butter of analog synthesizer emulation, but the other forms are also useful.

The Chamberlin filter has a pretty severe limitation in that it becomes computationally unstable as the cutoff frequency increases. Instead of keeping its output in a nice reasonable range of numbers, it goes exponentially out of range, which generally leads to a brief pop followed by silence. Usually it's a digital clipping sort of pop rather than a speaker-cone-ripping sort of pop, but still, not a good thing.

Chamberlin's book, Musical Applications of Microprocessors, neglects to mention this instability at all. It's well known in DSP circles, but I'm new to this whole thing, so only slowly began to grok the connections between discussions of stability limits and the misbehavior of my plugins. I've now known for a while that I needed to do something about it, and finally this week have managed to make the fix.

The basic approach is, since the stability limit is related to the digital sampling rate, to oversample within the filter, increasing the effective sampling rate, thereby increasing the stability limit. You can oversample by a little bit and add some hackery to help avoid the stability limit, or oversample by a lot and restrict the usable range of the cutoff frequency to ensure you never get to the stability limit. (I was restricting the cutoff freq range previously, but now I have a lot more range and a lot more margin of error available simultaneously.) I've now got implementations for both approaches in my filter library — they're each handy in different situations.

So, to take advantage of the new filter implementations, I've revisited some of my early plugins, Breathe Beat and Pegger, and released updated versions with the new filters and sundry other improvements.

Now, Breather, the new version of Breathe Beat, is hooked up to an emulated TR-808 and its output fed through a nasty reverb, and oh my goodness does it sound fabulous when the bandpass filter swoops down through 30Hz just as the 808 kick triggers. It's the kind of thing that makes otherwise reasonable people want to spend thousands of dollars customizing their pickup truck just to cruise around with it thumping out of their subwoofers. To tell the truth, I could do this with the old version too, but it somehow sounds better knowing that the code behind it sucks less.