1 Jul
2021
1 Jul
'21
7:45 p.m.
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