Re: Transfer function reduction math

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.