[sdiy] Vocoder dumb idea of the night

[jhaible at debitel.net]

Exactly my way to see things, too.
I just wonder if there is a competing definition established
(as for so many things).

JH.

> 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.
> 
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