On Thu, 3 Aug 2000, Larry Conklin wrote:

> > I also have been using digital filtering with one of my computers with an
> smt-8 > style vertical. I tried IIR filtering but ran into numerical
> stability problems. I > found better luck with multipole FIR filtering. I
> made a program in Basic to > create the filter coefficients for a desired
> shape and then have an option in my > data acquisition program to use the
> filter file created. It works quite well on a > 386. What I like is you can
> create various filter responses in different frequency > ranges and if this
> doesn't work for the noise you just change the coeficients not > the
> hardware. I am trying to have the program create it's own filter based on
> the > long term background noise. Currently this consideration is included
> in my trigger > routine.  > Regards > Barry
> 
> This is exactly the kind of thing I have been thinking about (except for the
> automated filter tuning).  I would be very interested in seeing your code if
> you would be willing to post it or send me a copy.  I have a pretty good
> background in analog active filter design but I know virtually nothing about
> digital filters. 

   Time domain filters are really just digital convolutions.  A filter in the
frequency domain is simply performed by taking some filter function and
multiplying it by your FFT.  The inverted FFT then gives you the filtered time
series (seismogram).  This operation is actually the same as a direct
convolution of a time series (i.e. the convolution theorem of Fourier
Analysis).  However, because of the digital nature of the problem, they do not
allow you to easily benefit from a lot of the techniques such as the use
of power spectrums without quite a lot of work.

   Non-recursive FIR filters (finite impulse response)  convolve your incoming
data with some finite time series and produces a new time series.  Recursive
IIR filters (infinite impulse response) do the same thing, but they also add a
convolution of the previous output values from the filter; i.e. they use
previous original and filtered data to perform the resulting data set.  The
instability in IIR filters happens when the dependence on the previous output
values becomes too strong for a set of data, which produces incredibly high
filtering for given frequencies.

One tough thing about using standard digital time domain filters is that you
may not want each seismogram filtered in the same manner, and after performing
some of these complicated convolutions it can be hard to recover the original
data.  That is why it is generally easier to mess around with data after the
fact in the frequency domain.  It is truly amazing what some of these
frequency filtering methods can do for a noisy data set.

For more information on this topic, see sections 12.5 through 12.10 in the
Nummerical Recipes book link that I posted previously.

******************************************************************************
John Hernlund
Department of Geological Sciences
Arizona State University
E-mail: hernlund@.......
WWW: http://www.public.asu.edu/~hernlund/
******************************************************************************

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