[sdiy] Analysis filter bank help

[Magnus Danielson]

On 05/10/2013 01:55 AM, David G Dixon wrote:
> 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.

Ehm... The "knee" is sharper with Chebyshev, but the roll-off as you get 
away from the cut-off is about the same as equal pole Butterworth or 
Linkwitz-Riley. Elliptic filters or any other where you move the zeros 
closer to the cut-off will have roll-off which is quicker, but with the 
draw-back of far-out damping, but with the zeros dropped around the 
spectrum it will be sufficient damping.

Cheers,
Magnus

> 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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