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

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?

https://ccrma.stanford.edu/~jos/spectilt/

https://ccrma.stanford.edu/~jos/spectilt/spectilt.pdf

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: dsp.stackexchange.com/a/56820/41790
– Ed V
Feb 15 '20 at 19:36

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)