[sdiy] Filter terminology question

[Magnus Danielson]

From: Mididood at aol.com
Subject: Re: [sdiy] Filter terminology question
Date: Thu, 20 Nov 2003 22:28:55 EST
Message-ID: <153.2716acf4.2ceee077 at aol.com>

> We're having fun now!

Indeed! ;O)

... and people complain that signal theory is booring! ???

> I said "...Oh well - I don't mean to raise Rod Serling from the dead or ..."
> 
> and got a:  ?????
> 
> Sorry for the (possibly to some) obscure reference - this rather famous
> American writer wrote the TV series "The Outer Limits" and then "Night
> Gallery" ...great little weird and usually sci-fi type vignettes - all about
> 'other' dimensions, realities, etc - very cool shows in their day.  Figure
> most DIYers over here would know - but I FORGOT this thing ain't strictly a
> western hemisphere/North American sort of deal.  I'm sorry - I'm so stupid
> sometimes...

Well, the mail-list server is somewhere in Netherlands (I haven't visit it but
I guess I am flying through there soon).

> Now if THIS doesn't help with the filter poles, tents...I don't know what
> will. ;)

Let's keep to the 3D views of amplitude response. An alternatively view is the
3D view on the phase-shift response, but that might be a little harder to
interprent mentally...

> But seriously - I'm almost thinking about getting my Laplace Transform books
> out and trying to recall all that stuff...a....duh - probably not tonight....
> 
> What I DO remember from it all is that it started out as an absolutely
> horrifying subject - taught by an incomprehensible instructor of a foreign (to
> me) dialect - and once I eventually sorted through the whole math 'transform' 
> S-domain thing, intensely painful at first, it was rather easy...to at least
> do well on the tests....I think I got an A in the end - But I still don't
> quite know what the heck I was doing it all for.  Guess this begs for my rehab
> on the subject!  and, ah - maybe make a filter?

I think you share the same experience as many other EEs do (possibly minus the
foreign instructor) in that yeah, yeah, we went that coarse but no, we don't
really recall much from it.

We know from various exercises in diffrential calculus that a first order
diffrential system can be solved with an A*e^(ot) where o is a real variable
(this is an overgeneralisation, there is a little more to it). We also know
that second order diffrential systems sometimes exhibit a solution of the style
A * (cos(jwt) + j sin(jwt)) and then also that a more generic set of solutions
exists in A * e^(ot) * (cos(jwt) + j sin(jwt)). This later can be transformed
into A * e^(ot) * e^(jwt) = A * e^(ot + jwt) = A * e^(st) where s = o + jw.

We also know that when we integrate a function multiplied with some other
function, we get the correlation between these two functions. If we now assume
that we have a function f(t) that is the result of a impulse responce from a
linear system (i.e. a fixed diffrential system of some degree) we can assume
that it contains the impulse responces of a number of A*e^(st) where we want to
establish both the A and the s for each of those. We also know that e^a/e^b is
e^(a - b) so if we want a perfect cancelation such that e^(a - b) is 1, then
must a - b = 0 or a = b. If now we let a be the s1*t of the function and b be
the -s*t of variables, then will the integration iron out A1 for the s1
position only when s is selected to be s1 since otherwise a <> b and then the
integration doesn't converge. The integration limits is fairly easy too, the
lower end is really - infinity, but since the Dirac-delta occurs at t=0 the
response prior to 0 must be exactly 0, so 0 is the begining in time, and since
we can theoretically have events being perfect solutions for (cos(jwt) +
jsin(jwt)) we have things going on into the infinity. This transform is a pure
linear transform, we only multiply and add/integrate so once we've done it for
one responce, we can combine any of them and make more complex responces if we
only allow for them to break up into pieces.

> Thats what you get for going to work for a power company after college,
> instead of Intel or Cisco, or something...laughs

They also work with power in about the same way (overgeneralising).

> Thanks for all data - I think "Filters 101,201, and 301" are all in the last
> several posts!

Possibly. But there is way more to say.

Cheers,
Magnus