Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: "Don" <g@crcomp.net>
Newsgroups: sci.electronics.design
Subject: Re: Transfer function reduction math
Date: Wed, 12 Jun 2024 03:17:43 -0000 (UTC)
Organization: A noiseless patient Spider
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Message-ID: <20240611b@crcomp.net>
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bitrex wrote:
> Don wrote:
>> bitrex wrote:
>>
>> <snip>
>>
>>> Seems like they're doing some kind of tanh interpolation but it's not
>>> entirely obvious to me how they get from equation (3) to the expression
>>> in (5).
>>
>> Unless the fuzzy form of your scan deceives my eyes, it appears the
>> numerator and denominator are multiplied by the conjugate to obtain
>> (4) from (3).
>>
>> A clearer scan may enable me to continue.
>>
>> Danke,
>>
>
> (not sure if my response posted as I don't see it on my newsreader,
> apologies if this reply appears twice)
>
> Sure, here's the full page in question:
>
> <https://imgur.com/a/as3jfNo>
>
> I have a hardcopy from an academic library which is a relatively massive
> (800+) page tome so difficult to get a good scan of...the only full-text
> online I can find is on Springerlink (blech) and despite my having an
> "institutional login" that should grant access to it. it never seems to
> work with them.

Your first followup was indeed posted.

The first three steps from (4) to (5) are easy-peasy:

    tanh(s) = (e^s - e^-s) / (e^s + e^-s)
    H(s) = Q(s) / D(s) = (e^s - e^-s) / (e^s + e^-s)
    (e^s + e^-s)Q(s) = (e^s - e^-s)D(s)

Control Theory must now be reviewed by me in order to continue.

# # #

"Lecture Notes in Control and Information Sciences" seems to be a series
of books, each about three hundred pages long. Where do you find page
808?

Danke,

-- 
Don, KB7RPU, https://www.qsl.net/kb7rpu
There was a young lady named Bright Whose speed was far faster than light;
She set out one day In a relative way And returned on the previous night.