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?



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

  • $\begingroup$ 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 $\endgroup$
    – Ed V
    Commented Feb 15, 2020 at 19:36

1 Answer 1


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)


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