Is a "Spectral Tilt Filter" the best way to get an arbitrary slope and cutoff LPF?

Question

I need an arbitrary slope audio LPF for which both the cutoff frequency and slope in dB/oct can be smoothly modulated in real time.

Is the "Spectral Tilt Filter" described by Julius Smith the correct or best way to do this?

If so has anyone implemented this in C++ before or would it be hard to do?

Exponentially distributed poles and zeros are what Corsini and Saletti used in their filters. See this link for the reference: https://dsp.stackexchange.com/a/56820/41790 — Ed V, Feb 15 '20 at 19:36

score 1 · Answer 1 · answered Feb 16 '20 at 03:34

yeah, that's the way we've been doing pink noise filters (or "pinking filters") since the 80s.

if you ignore edge effects it's made by alternating these pole functions:

$$ \log|H_{2k}(j\omega)| = -\tfrac12 \log\left( 1 + (\tfrac{\omega}{p_k})^2 \right) $$

and these zero functions:

$$ \log|H_{2k+1}(j\omega)| = \tfrac12 \log\left( 1 + (\tfrac{\omega}{q_k})^2 \right) $$

and the total frequency response is

$$ \log|H(j\omega)| = \sum_n \log|H_{n}(j\omega)| $$

(this is not done yet)

1 Answers1