Well, it is sort of a catch-22. If you already know what the signal
looks like, then you're already done. But being close is better than
being far away. The Wiener filter itself is described in the Undisputed
Source of All Human Knowledge here:
http://en.wikipedia.org/wiki/Wiener_filter
As for a well-defined measure of the goodness of a filter, the best
metric is to compare the result of the filtration to a known "right
answer". If you don't know the right answer, then the next best thing
is to make one up that is as close as possible to what you believe the
right answer "should" look like, add to that your best guess of the kind
of noise you are dealing with, and then try different filters on your
fake data to divine the best way to recover the uncorrupted signal.
Then you can "blindly" apply that "best filter" to the real data. After
all, the only difference between signal and noise is that you find the
signal interesting. Your detector doesn't know the difference. To
separate the two you may find that you need to learn as much about the
noise as you do about the signal, and that is what the concept of
"optimal filtering" is all about.
HTH
-James Holton
MAD Scientist
On 8/29/2014 2:57 PM, Keller, Jacob wrote:
That is, the optimum noise filter is generally the same shape as the signal of
interest ...
Has this been proven, or it just common sense? And if the filter is the same
shape as the signal, why does one need the signal at all? I guess I don't know
precisely what you mean, but anyway, I like the concept, which seems to have a
sort of Bayesian aroma to it.
I'd also be interested to know of a well-defined and useful measure of the
goodness of a filter.
Good weekend,
Jacob Keller
