On Thu, Jul 01, 2021 at 02:08:45PM +0200, David Kastrup wrote: > Isn't any LTI filter with conjugated pole pairs (Q > 1 or some other > simple constant I'd need to look up) resonant in that it produces a > decaying sine with fixed frequency (for each such pole pair) A conjugate complex pole pair is indeed almost a definition of 'resonance'. Which also corresponds to a second order linear differential equation with a negative discriminant. Such resonances occur easily in physical systems, all you need is a restoring force proportional to displacement, Then Newton's law F = m * a results in an acceleration proportional to minus displacement. Acceleration is the second derivative of displacement, so the result must be a function which has a second derivative proportional to minus the function itsef. The second derivative of sin (w * t) is - w^2 * sin (w * t), so that fits the bill. > when its input is switched off? Not just then, for any transient input. The impulse response is an exponentially decaying sine wave. For a formant filter such resonances are the obvious choice, but as a filter bank meant to separate a signal into almost non overlapping bands they are not very useful. To get e.g. the IEC class I octave or 1/3 octave bands you need at least 6th order. Ciao, -- FA _______________________________________________ Linux-audio-user mailing list Linux-audio-user@xxxxxxxxxxxxxxxxxxxx https://lists.linuxaudio.org/listinfo/linux-audio-user
