[sdiy] Filter topology: n-order == n-poles?

[JH.]

>I am reading Timothy Stinchcombe's analysis of the Korg MS-10 and
>MS-20 filters, and was reminded of a question that's been in the back
>of my mind for a little while.  Filter users typically refer to a
>filter's number of poles, where each pole seems to add -6dB/Octave to
>the cutoff slope.  Filter designers and mathematical types tend to
>refer to the "order" of the filter, e.g. "2 cascaded, buffered
>1st-order sections" in the Korg MS filters.  Is a 2-pole filter
>necessarily a 2nd-order filter, or is the relationship more
>complicated?  Thanks for answering this rather basic question...
>thanks!

Normally, number of poles = order, per definition. regardless of filter 
type,
with a possible exception:

Band pass filters _should_ follow this rule also, but part of the literature 
doesn't follow
this convention, calling a BPF with N pole _pairs_ a filter of Nth order.
>From what I've learned, this is wrong. But there could be this reasoning 
behind it:
You get HPF and BPF functions, starting with a LPF function, applying 
so-called
LP-HP and LP-BP transformations. These transformations turn a N-pole LPF
into a N-pole HPF, and into a 2N-pole BPF, respectively. So the reasoning 
goes
that these 3 are of the same class, namely "Nth order".
Sounds reasonable, as long as you don't create a 2N-pole BPF from a N-pole
LPF and N-pole HPF in series. Why should the _same_ filter function be 
called Nth order
when it's made of N 2-pole BPF's, and be called 2Nth order, when it's made 
by
a a series connection of two Nth order filters, one LPF and one HPF?! 
Doesn't make sense.
You'll sometimes find it used that way, nevertheless.


JH.