[sdiy] Filter terminology question

[Tim Stinchcombe]

Aaah, this one again. I think there was a lot of chit-chat about this on
sci.electronics.design a few months back.

> 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 
.
.

Useful as an analogy it may be, but there is no way that this is the reason
why poles are named such. Geometry and complex analysis are riddled with
references to 'poles' and 'polar' etc. I would imagine (I admit I don't know
for sure) that it probably derives from projecting points on a sphere onto a
plane - stick a 'globe' on a plane, so the south pole is at the origin of
the plane. Project a line from the north pole, through the sphere, and down
onto the plane. There is then a one-to-one correspondence between points on
the sphere, and those on the plane. But the north pole itself is a tricky
one, because its projection is parallel to the plane, and therefore it meets
the plane 'at the point at infinity'. Doubtless this got adopted into
complex numbers et al, so that our filter pole, being zero in the
denominator of the transfer function, makes the whole thing shoot off to
infinity. The ancient Greeks were probably sketching such things in the sand
thousands of years ago, blissfully unaware that rubber sheets on tent-poles
was a handy way of looking at it.

If you draw a circle with two tangents, then the point where the tangents
meet is called the 'pole' of the line between the points of contacts of the
tangents, this line being called the 'polar' of the point. This is similar
to the above, and again one can see that there is a problem when the 'polar'
is a diameter, so that the 'pole' is the point at infinity. :-)

Tim
__________________________________________________________
Tim Stinchcombe 

Cheltenham, Glos, UK
email: tim102 at tstinchcombe.freeserve.co.uk