--_003_AANLkTim9dkCeGxR5oYmACC0tDM8dJqYnN8HRZpoC3YOmailgmailco_
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> So you can give it new names, but you're really just computing the
> average of the last N samples. =A0(now, if there's a lot of difference
> in samples, you might notice that recent samples have more "weight"
> than older samples, but that's just a little detail...)

I'll quibble gently.
I know you know, and your comment further reflects the knowledge, but
I think a better way of putting it would be something like:

'The "average" of ALL prior samples + the  latest sample, with the new
sample being given a "weighting" of 1/Nth of the new "average" '.

Note that "average" here does  NOT have the same meaning as 'average'
usually does.
Olin explicitly addressed this with his signature "do you really want
to keep all N sample". I didn't think so".
Readers are free to decide whether his "I didn't think so" is valid
for them - and in many cases it will be - but by making this decision
you have a MUCH different beast than an average over N samples.

What this is, as has been noted, is a single pole exponential function.

With a true N samples average you start dropping off whole prior
samples N periods after they have happened. With the exponential
function you drop off only an Nth of the effect of a sample N+1 ago.

That they can be very different in response is easily seen by graphing
some typical step responses. I just produced  some Excel graphs with
varying N lengths and step functions of Y samples =3D 1 and all others =3D
0.

A graph of only one such is attached.
Blue curve is input step.
Octarine curve is true average
Yellow curve is exponential filter under discussion here.

Do you think they are identical? I didn't think so :-).

Whether this matters depends on application. Input function can make a
large difference.

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).

The exponential function has the advantage of starting up properly
from 1st sample whereas true averaging needs either a sliding length
for the 1st N samples or some other handling of its boundary
conditions. "Horses for courses".


        Russell

--_003_AANLkTim9dkCeGxR5oYmACC0tDM8dJqYnN8HRZpoC3YOmailgmailco_
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