Olin Lathrop wrote:
> RussellMc wrote:
> > I have used the exponential filter extensively in the past BUT it has
> > such sluggish performance under some conditions when it is usually but
> > not always useful that I sometimes add ad hoc rules to it to modify
> > its behaviour. eg priming it with current sample value on input would
> > be one possibility (depending on input function).
>=20
> The tradeoff between random noise attenuation and the step response of a
> single pole filter is fixed.  No free lunch to be had.  However, you can
> significantly decrease the step response at the same random noise
> attenuation by cascading multiple filters.  This may sound like a free
> lunch, but it's not since the computation requirements have gone up.
> Fortunately single pole low pass filters are relatively easy to compute, =
so
> using multiple poles is often a good option.
>=20
> To illustrate this, I plotted the step response of two filters with the s=
ame
> random noise attenuation but with different numbers of poles.  The algori=
thm
> for each pole is as described previously:
>=20
>   FILT <-- FILT + FF(NEW - FILT)
>=20
> For the single pole, FF =3D 1/16.  For the 4 pole case, FF =3D 1/2 for ea=
ch
> pole.  Note that the product of all FFs for each filter is the same.  The
> step responses are dramatically different however, as you can see in the
> attached image.

Olin, I have to ask, in what sense do these filters have "the same random
noise attenuation"? It's pretty clear that they have different bandwidths
and different cutoff slopes. I don't see the significance of having the FFs
multiply out to the same value in both cases.

-- Dave Tweed
--=20
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