Should the slope of your filter be 6, 12, 18 or 24 dB per octave?

Low-pass and high-pass filters often have a 'slope' control. What is the slope of a filter? How do you select the right slope?

Pass band and stop band

A low-pass filter, for example, is a circuit (or digital equivalent) that allows low frequencies to pass and cuts high frequencies. What's interesting is what happens in the transition between pass and cut.

Most filters do not simply pass certain frequencies, then suddenly at a certain point cut the rest of the frequency band completely. A so-called 'brick wall' filter is neither useful nor sounds good in most circumstances.

Instead there is a 'pass band' in which signals get through unaltered, then a gentle transition to the 'cutoff frequency' where the level is 3 dB lower than in the pass band. Then the response falls off further and further down into the 'stop band'.

6, 12, 18, 24 dB/octave slopes

If the simplest possible filter is constructed from electronic components - one resistor and one capacitor - then the rate at which the level drops in the stop band will be 6 decibels per octave.

This means that for each successive doubling of frequencies above the cutoff frequency, the response falls 6 dB. (This is the same as saying 20 dB per decade - a drop of 20 decibels for every tenfold increase in frequency).

A slightly more complex filter design can achieve 12 dB/octave; further increases in complexity can yield 18 dB/octave and 24 dB/octave. Oddly enough, in-between values are more complex to achieve, and therefore pointless to attempt.

What use are these different filter 'slopes'?

A 6dB per octave slope is useful for gentle shaping - a little less bright, a little less heavy, depending on whether the filter is high-pass or low-pass. 12 dB/octave is more useful in a creative musical context. 18 dB/octave even more so as you can cut out great swathes of frequencies and hear hardly anything that you don't want left behind.

24 dB/octave is a little harsh for most purposes. It's like a cliff edge rather than a steep hill, and you can hear the 'edge' where the response suddenly starts to fall.

24 dB/octave in synthesizers

However in synthesis - subtractive ('analog') synthesis, then 24 dB/octave is perfect as it can remove high frequencies while still leaving 'bite' in the sound. Some synthesizers have filters with even steeper slopes.

Filters in loudspeakers

Loudspeaker crossovers also have filters. 12 dB/octave and 18 dB/octave slopes are commonly used to separate bands of frequencies between woofer, mid-range and tweeter. The steeper 24 dB/octave slope is usually only found in PA systems where an active crossover (for which a 24 dB/octave filter is easier to implement) divides the frequency bands before the signals pass through to the power amplifiers.