[SI-LIST] Re: Kramers-Kronig in Pictures
- From: <colin_warwick@xxxxxxxxxxx>
- To: <Peter.Pupalaikis@xxxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Fri, 11 Dec 2009 09:44:54 -0700
Hi Peter,
Thanks! Kramers-Kronig goes back to the 1920s of course. You can see the more
recent Hall and Heck treatment that got my creative juices flowing in the
preview at Google books:
http://books.google.com/books?id=AB2DHvhSHpsC&pg=PP331#v=onepage&q=&f=false
...or you could buy their book of course :-)
If you don't have a blog, I recommend http://drop.io as a place to upload stuff
to. They give you a shortened link for your upload. You can post the link as
plain text to the si-list. It's free up to 100MB per link.
Discrete Fourier transforms like FFT have some well known limitations (Gibbs,
Nyquist,...) compared to the infinite frequency Fourier integral. FFT has
obvious pros too, like being efficiently computable.
Cheers!
-- Colin
-----Original Message-----
Colin:
I'm not sure how much of your material or presentation style is original,
but the material you presented was
the clearest I've seen and it has sparked some further thinking and
experimentation with these concepts. I've thought
and read about this before, but it's the first time that I feel like I have
a handle.
Thanks for sharing this and I recommend it.
I have a small MathCad spreadsheet that shows what is meant by your
material as it pertains to the FFT, which is
what we're all using at some point, I suppose. I'd like to share it
somewhere but haven't figured out how yet.
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of WARWICK,COLIN (A-Americas,ex1)
Sent: Thursday, December 10, 2009 10:09 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Kramers-Kronig in Pictures
Hi,
Thanks to Eric Bogatin for pointing out a neat proof of the Kramers-Kronig
relation in his excellent book review:
http://bethesignal.net/blog/?p=63
...of Hall and Heck's excellent book.
After some reading and doodling, a little light bulb lit up, and the result
was my latest blog posting "Kramers-Kronig in Pictures" here:
http://signal-integrity.tm.agilent.com/wp-content/uploads/2009/12/Kramers-Kronig-in-Pictures.htm
The Kramers-Kronig relation is very useful in SI because it enables you to
determine time-domain causality (or lack thereof) of a frequency domain
model (e.g. s-parameters) before you attempt to move it into the time
domain. IMHO, it's worth getting to know.
Hth
-- Colin Warwick
Signal Integrity Product Marketing Manager, Agilent EEsof EDA
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