# IIR filters with variable roll-off

I have a filter design problem in which lowpass filters have to be designed with varying roll-off. E.g: 2.7 db/ocatve or 1.4 db/ocave. See picture below.

This is easy to achieve with a FIR filter, yet its computational cost is too large. Therefore, if at all possible, I would like to do this with an IIR filter. Sadly, most IIR filters have multiples of 6dB/octave rolloff.

• You can design the filters numerically for different slopes and make tables of their coefficients or other numbers that determine their coefficients. Then in your run-time filter, interpolate between those numbers to get some intermediate slope. Some filter forms may have stability problems when changing the slope rapidly so do explore different filter forms. Feb 29, 2016 at 7:46
• You are saying that interpolation of IIR filter coefficients works ? I don't believe that is the case. Well, actually, I once tried that and the results are horrible filters that are not even nowhere near to what you would expect. If it were that simple there would be lots of recipes on iir filters with rolloffs other than multiples of 6 dB/octave.
– user7488
Feb 29, 2016 at 8:25
• I have had similar bad experience interpolating IIR filter coefficients, but I think with the right filter structure (maybe all-pass based) coefficient interpolation or interpolating something like pole and zero loci or the cutoff frequency of high-shelf sections might work. Do you need to vary the cutoff and/or the roll-off as a function of time (= time-variable/varying parameters)? Feb 29, 2016 at 9:33
• Here's a related question: How to design a variable slope highpass filter May 18, 2017 at 19:03
• This answer probably also answers this question. Jan 27, 2018 at 14:22