# LPF/HPF Filter with 15db/octave

I want to make both, LPF and HPF with 15db/octave.
I found a topic where someone could do that with 36db/octave

But I can’t figure out how to make it with a number that isn’t a multiple of 12 like 15db/octave. Any help will be appreciated!

I don’t know of any simple way to get a slope that is not a multiple of 6. For even multiples of 6, you chain 2-poles. For odd multiples, you chain 2-poles and a 1-pole at the end. The computation of coefficients gets tricky for high orders though. I think there’s a function to get them for Butterworths in the dsp namespace.

One method is to use a shelving filter and compute a shelf gain that gives you the desired slope. For example take a high shelf filter:

Fc = 1kHz, cutoff frequency
Fs = 48kHz, sample rate
G = gain at F == Fs
dG = -15, difference in gain per octave in decibels per octave
dF = log2 (Fs / Fc), the difference in frequencies in octaves

G = dG * dF = -15 * log2(48k / 1k) = -83.7dB

So if you make a highshelving filter with a gain of -83.7dB that begins to filter at F = 1khz, you’ll approximate a 15dB/octave lowpass filter.

I believe this is the same technique described in this paper but my AES membership has lapsed and I can’t confirm that. That design goal was to preserve the stopband attenuation at nyquist for LPFs though, through mimicking a LPF using a high shelf.

Thanks for your answer , please, could you tell me how can I do a filter of 6db/octave?

Thank you for your detailed response!!