[sdiy] Filter terminology question

[Magnus Danielson]

From: Mididood at aol.com
Subject: Re: [sdiy] Filter terminology question
Date: Thu, 20 Nov 2003 14:02:27 EST
Message-ID: <12b.3580e971.2cee69c3 at aol.com>

Hi Rog,

> Interesting and highly informative discussion on filter hubbub...
> 
> One thing I though may be of assistance - and please excuse if this was
> mentioned as I didn't go back too far in the thread...
> 
> I did some time ago (understatement..) get a BSEE - and of course had the
> 'filter theory'  classes, etc...bla,bla,bla..
> 
> I could never get my mind around this term: 'pole'.
> 
> I then, quite recently came across a fantastic explanation of how this term
> came to be used in the first place and it all cleared up for me...I hope this
> isn't too naive or basic on my part...
> 
> The term 'pole' comes from the concept of a 'Tent Pole' and how -assuming
> you've seen a big circus tent or whatever - have a pole sticking up in the
> middle and you get that 'response' curve which we usually look at in the 2D
> plane for f'ilter response curves',  but in the 'cloth' of the tent, is
> actually a 3D thing - actually the 'pole' represents a characteristic of the
> filter response

To be exact, it represents the amplitude response. The complex response would
create a 4D shape, which is a bit annoying to display to stupid 3D-space
1D-time critters like humans.

> (the Q or center freq. of that particular 'pole'), in a 3D
> plane such as that seen when you stick a 'pole' up under a tent and getting
> the 'draping-off' pattern around the whole 360 degrees of the pole - usually a
> log type of slope - so a 3 pole filter, per se, has 3 tent poles sticking up
> at the freq centers (Qs) predetermined by its design, and a 'drop off'
> depending on their degree of cutoff-slope -or 'order'  -   much of this has
> already been eloquently said so I'm not even gonna try and reiterate here - my
> minds pretty fuzzy these days!  I hope I got it right - please excuse if I've
> confused it any worse....

Not quite... this would be true for a 3-pole filter with real-only poles.
For a 3-pole filter where 2 of the poles are complex, then those two poles
will be quite separate from each other, and also from the 3rd pole which is
stuck back at the real axis. This means you have 3 poles sticking up under the
tent.

By the way, one of the first matlab hacks I did was to make a 3D plot of
filter responces, including a 5-pole/5-zero Butterworth allpass filter.

The zeros creats dips in the tent, dips down to 0 in amplitude (- oo in log-
scale, which is convenient).

> But I hope that helps in a visualization of the concept of a filter "Pole"
> 
> Happy Camping....

Ouch!

Cheers,
Magnus