[sdiy] Vocoder dumb idea of the night

[Czech Martin]

In my understanding the order of a linear system that can be described
via differential equation is the order of the DE.
This is equal to the number of poles, the number of eigenfunctions
and their eigenvalues resp. the number of roots of the char. polynomial.
The number of zeros is not important.

Also the order is related to the number of Cs plus Ls.
I mean this in the ideal circuit schematic sense, I know
that real components have already some additional
parasitics inside, so the actuall order is much higher.

E.g.: the state var is 2nd order, and it has two Cs (and no Ls).
In reality each op amp will have at least 3 poles inside,
so most state var filters are actual 11 pole or 14 pole systems.
Since the additional poles are (hopefully) out of the audio
band, we tend to neglect them.
The idea of order vs. components becomes more clear in passive
RLC filters.
 

The resulting transmission function can have a lot of shapes.
The low freq. slope could fall of faster then the high frequ.
slope. 

So order really doesn't say much about the transfer function.

There could be pathological situations where a zero will exactly
cancel a pole. However, in practical cases we know that this
will not happen exactly, so this kind of order reduction
is not a major obstacle. Inserting a zero is allways connected
with inserting some poles, since all real systems are lowpass
in the high frequency end.


m.c.



-----Original Message-----
From: jhaible at debitel.net [mailto:jhaible at debitel.net]
Sent: Mittwoch, 14. Mai 2003 12:29
To: xyzzy at sysabend.org
Cc: Czech Martin; synth-diy at dropmix.xs4all.nl
Subject: Re: [sdiy] Vocoder dumb idea of the night


> On Wed, May 14, 2003 at 10:04:12AM +0200, Czech Martin wrote:
> > A 2N order bandpass has N*6dB fallof for higher, lower frequencies.
> > 2nd order means 6dB, 4th order means 12dB. Arround the peak it can be more
> > due to high Q.
> 
> I dont know why I always get Order and Pole confused. *sigh*

I also think Martin's definition is right. (a SVF for instance doesn't
change its order if I go from the 12dB LPF output to the 6dB BPF
output !) But nevermind: One of my filter design programs also
uses a different definition (where a 12dB BPF is called "2nd order")

Maybe there are two competing definitions.
The SVF example supports the "2nd order BPF = 6dB/Oct slope" point
of view. But there is also a design method for BPFs and HPFs that
starts with a LPF and then does a LPF->BPF or LPF->HPF transformation.
While in the LPF->HPF case the order and slope is preserved, I
_think_ (please double check!) in the LPF->BPF transformation
the slope is preserved and the order would then be doubled.
And here I can see a reasoning that you would define "order"
in an alternative way, where LPF->BPF transformation also preserves
the filter order.
I don't know if there is a definition / argument for that second
case. But while I could understand the reasoning behind it, I feel
more comfortable with the definition that just counts filter poles.

JH.

-------------------------------------------------
debitel.net Webmail