[sdiy] Analysis filter bank help

[cheater00 .]

Hi Richie,
if this is digital, just sum up your band pass outputs, deduct them
from the input, and what's left is the upper and lower bands mixed
together. Then use a simple cross-over which centers somewhere in the
middle of the dead zone, one such that the pass-band has no phase
shift.

Cheers,
D.

On Fri, May 10, 2013 at 12:41 AM, Richie Burnett
<rburnett at richieburnett.co.uk> wrote:
> Hi all,
>
> I'd like to pick the collective brains of this list's members, if I may.
> It's a question about analogue filter design...
>
> I currently have an analysis filter bank designed for a Vocoder (will be a
> DSP implementation eventually.) Currently this consists of 20 bands.  Each
> of these is an 8th-order bandpass filter with 1/3rd octave bandwidth.  These
> filters are Linkwitz-Riley filters (sometimes called "Butterworth squared".)
> This ensures that adjacent filter band responses are both 6dB down and
> in-phase where bands meet, with the intention of getting the outputs of the
> entire filter bank to add up to a flat frequency response.  So far this
> works very nicely.  The resulting 20 analogue band-pass responses sum to a
> flat line with about +/-0.5dB ripple.
>
> Now here's the catch.  I want to change the bottom filter band to be a
> low-pass response, and the top filter band to be a high-pass response.  Then
> these two filters will catch everything below, and everything above the main
> bank of 18 remaining bandpass filters.  My intuition was to design these to
> be Linkwitz-Riley low-pass and high-pass responses respectively, but when
> their outputs are summed with the other 18 bandpass filters the result
> doesn't add up anywhere near to a nice flat response!  In fact the very
> gradual roll-off of these L-R filters wrecks the summed response anywhere
> near each end of the filter bank.
>
> I took a look at the excellent web page of Jurgen Haible about his Vocoder,
> and notice that his lowest and highest band's filters are lowpass and
> highpass like I want to implement.  However, their frequency responses seem
> to be Chebyshev type-1 responses.  I'm not sure how he arrived at this
> revalation to use Chebyshev filters for the lowest and highest bands, and
> unfortunately can't ask him.  So, can anyone explain to me the maths behind
> how this works?
>
> Also, whilst Jurgen's Cheby low-pass and high-pass filters incorporate into
> the bank to give a relatively flat response compared to my attempts, I'm
> still a little concerned about the quite leasurely rate of roll-off in the
> stopbands for these filters at each end of the bank:
>
> http://www.jhaible.com/vocoder/living_vocoder.html
>
> I'd really like to understand what's going on here if someone can explain,
> or can point me towards some useful references.  Everything is simulations
> of Laplace functions for me at the moment, so I'm happy to talk maths
> instead of circuits if that's what's required!
>
> Many thanks for reading,
>
> -Richie Burnett,
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