X-Pole Super Smother


A Super Smoother filter from John Ehlers' book "Cybernetic Analysis for Stocks and Futures: Cutting-Edge DSP Technology.

A Pole is a single-frequency point of pushing gain up, and a zero is a single-frequency point of pulling the gain down; with a single pole, you are not going to get complex response curves such as bandpass, peak, and shelving filters that you can get with the two poles and zeros of a biquad. That leave us with lowpass and highpass, which have a single point of change.

However, a One-pole makes a poor highpass filter for cases in which we might be likely to use it—in particular, a DC blocker.
That’s because it makes a highpass by pushing response up at high frequencies—we really need a zero to pull the response down at very low frequencies.
So, we’ll only implement coefficient calculation for lowpass response here. However, we can still make a highpass filter suitable for a DC blocker by subtracting the output of a one-pole lowpass filter, set to a low frequency, from the direct signal.

The 6 dB per octave slope of the one-pole filter—a halving of amplitude for every doubling of frequency—is gentle and natural. It’s extremely cheap, computationally, so it’s the perfect choice when you need just a bit of smoothing. And it doesn’t “ring” (overshoot), so it’s an excellent choice for filtering knob changes. Run each of your user interface sliders and knobs through a one-pole lowpass set to a low (sub-audio) frequency, and your glitchy, zippered control changes turn into smooth parameter changes.