Hello all,
I've been studying the implementation of the 3rd order elliptic (Cauer)
lowpass filter in the Filter library (such as defined here
https://github.com/oknytt/faust/blob/551d63a27e5853ec911b5f4d9fabfcd09885a117/libraries/filter.lib#L1394),
and I'm confused about the derivation of the second- and first-order filter
coefficients.
I understand the analog prototype designed with `[z,p,g] =
ncauer(Rp,Rs,3);` in Octave, and I think I have a good understanding of how
to factor the transfer function into cascaded first- and second-order
sections. What I don't understand is the use of `poly` in Octave to find
the coefficients, and why the frequency of this elliptic filter is only
governed by the last coefficient in the final first order filter?
Intuitively it seems like so many more of those coefficients should depend
on the frequency of the filter, especially if we were to consider multiple
sample rates. My knowledge in this domain is fairly rudimentary, but are
there some assumptions here that I'm missing?
I've asked the same question on StackExchange (
http://dsp.stackexchange.com/questions/38095/analog-filter-prototype-to-direct-form-second-order-cascade)
as I understand that this list might not be the best place for this
discussion, but any explanation you can offer me here would be greatly
appreciated!
Cheers,
Nick
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