A high-pass filter with resonance.

## Overview

This is a digital simulation of the Moog ladder filter in a high-pass configuration with 4-poles (24dB/octave) and non-linear saturation in the feedback loop.

Frequencies below the cutoff are attenuated while leaving the frequencies above the cutoff (mostly) unchanged. The cutoff frequency is controlled by the combination of f0 and V/oct controls, while the bandwidth is controlled by the Q control.

This filter will resonate at high values of Q.

## V/oct

Pitch
Transpose fundamental by an amount in cents.

This parameter is used to transpose the base frequency up or down via a pitch CV (i.e. a signal that is calibrated to 1V/oct, typically one of the inputs from the ABCD matrix). In other words,

$\text{f} = \text{f0} * 2 ^{\frac{x}{1200}}$

where

• $$x$$ is the value of this control (in cents)
• $$f0$$ is the base frequency (set via the f0 control)
• $$f$$ is the final output frequency of the oscillator

For example, if the base frequency (f0) is set to 55Hz and this V/oct parameter is set to 2400¢, then the resulting frequency will be 220Hz or 2 octaves above 55Hz:

$220\text{Hz} = 55\text{Hz} * 2 ^{\frac{2400}{1200}}$

Modulating this parameter corresponds to exponential FM.

## f0

Gain/Bias
Set the fundamental (cutoff) frequency in Hz.

This parameter sets the fundamental frequency that is subsequently transposed by the V/oct parameter. Modulating this parameter corresponds to (thru-zero) linear FM.

### Q

This parameter controls the filter’s resonance. Resonance is the result of a soft-limited feedback path. This parameter sets the gain on that feedback. Higher values of Q (i.e. more feedback) yield a steeper roll-off but cause frequencies around the cut-off to be accentuated. The filter will resonate at Q-values exceeding 0.5 to 0.6.