[sdiy] Analysis filter bank help

[David G Dixon]

Chebyshev filters are known for steeper rolloff.  Indeed, an 8th-order
Chebyshev filter has the same rolloff as a 19th-order Butterworth filter.  A
Chebyshev II filter has a less steep rolloff, but no ripple in the passband.
An elliptic filter would have an even steeper rolloff than a Chebyshev
filter.

I'm not sure you're going to do much better.

> -----Original Message-----
> From: synth-diy-bounces at dropmix.xs4all.nl 
> [mailto:synth-diy-bounces at dropmix.xs4all.nl] On Behalf Of 
> Richie Burnett
> Sent: Thursday, May 09, 2013 3:41 PM
> To: synth-diy at dropmix.xs4all.nl
> Subject: [sdiy] Analysis filter bank help
> 
> 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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