Thread: Fwd: polezero option

Dear All -

My rewrite will arrive in a separate posting anon. Some comments on
Arthur's:

On 26 Apr 2009, at 14:26, Arthur Snoke wrote:

Thank you George and Kuang-He for comments. Kuang-He picked up on a
typo in the equation I wrote. I wrote him off list with a corrected
version that he said was okay:

(s-z1)*(s-z2)*...*(s-zn)
________________________

(s-p1)*(s-p2)*...*(s-pm)

...

%%%filters aren't causal, either!

The polezero transfer functions are analog filters and in themselves
are causal.

The analog filter response that the pole-zero description represents is
causal, but pole-zero descriptions are not necessarily causal. That's
the statement that I wanted to correct -- am I wrong?

The one I give as an example is an STS-2 response function, which is
mostly a damped harmonic oscillator. (Aside: I have read that there
are three versions/generations of STS-2 seismometers, but so far as I
can tell the analog-stage response is always the same. Can anyone
clarify?)

%%%Using TeX-style expressions isn't a good idea -- it assumes the
reader %%%knows TeX, when many use nothing more than Word to typeset
equations.
%%%Lay them out graphically in text, assuming a fixed-pitch font.

As of now, SAC help files use 7-bit ASCII. The minimal use I made of
TeX notation should be transparent to anyone who understands what a
Laplace transform is.

I don't see a connection between knowing mathematics and knowing TeX.
I know mathematics but typeset them with eqn/troff. See my own rewrite
in a separate message.

...

u: READ ABC.Z

u: TRANSFER FROM POLEZERO SUBTYPE SRO.PZ TO NONE

I do not use SAC to do my instrument correction, but I do use polezero
files. The above example as written would probably get one in trouble
at very low frequencies, as all seismometers have zero response at
zero frequency.

SeisMac doesn't! It is an accelerometer, but that can be a
seismometer, too.

If I understand the notation correctly, "FROM" means a deconvolution,
which means it divides the input waveform by, in this case, the
polezero expression. To avoid the output blowing up, this expression
should be amended to include the FREQLIMITS option. Putting these in
definitely makes the total transfer function noncausal.

So are pole-zero responses acausal, or are only band-limited ones
acausal?

George Helffrich
george<at>geology.bristol.ac.uk