[SAC-HELP] Fwd: polezero option
George Helffrich
george at gly.bris.ac.uk
Mon Apr 27 05:26:47 PDT 2009
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
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