[sdiy] Obtaining Bandpass and High-Pass Functions From A Four-Pole Low-Pass

[David G Dixon]

Mark,

To get proper bandpass responses from a cascaded-stage four-pole filter, you
have to sum the (input + feedback) signal in to the pole mixer as well.

If we take the following gain factors for {Input+Feedback, Stage 1, Stage 2,
Stage 3, Stage 4}, 4P HP mode is obtained when those gain factors are
{1,4,6,4,1}.  Also note that every other signal is inverted in the list.
Sum those up and you'll get 4P HP with the transfer function s^4/(s+1)^4.
The Intellijel Polaris filter (which I designed) gets this HP mode as well
as the 1P, 2P, and 3P modes, plus about 20 other useful modes.  I can send
you a list of all the necessary gain factors if you're interested.



> -----Original Message-----
> From: Synth-diy [mailto:synth-diy-bounces at synth-diy.org] On 
> Behalf Of mark verbos
> Sent: Monday, October 15, 2018 2:53 AM
> To: synth-diy at synth-diy.org
> Subject: [sdiy] Obtaining Bandpass and High-Pass Functions 
> From A Four-Pole Low-Pass
> 
> Hallo,
> 
> A while back there was talk about getting a hipass response 
> using cancellation of a lopass filter. I was surprised to 
> find out that you cannot simply cancel a 4 pole lopass to get 
> a 4 pole hipass. In fact, I still can't really understand 
> why. But, I was reading Electronotes about something 
> unrelated and I discovered an article about just this subject. 
> 
> In Electronotes #85 there is a technique for getting a 4 pole 
> hipass from a 4 pole lopass by mixing all 4 pole outputs. I 
> still don't really understand the math, but it is proven in 
> this article. As far as I can see, the Oberheim Xpander 
> filter doesn't ever get a 4 pole hipass. So, this may be the 
> only implementation of one using pole mixing. 
> 
> Mark
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