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

[rburnett at richieburnett.co.uk]

To get a 4-pole high-pass filter response you have to take a weighted 
sum of all 4 stage outputs plus the original input.  This produces a 
fairly decent high-pass response provided you use very tight tolerance 
resistors to get exactly the right mixing ratios for the five signals.

The reason why you can't get a 4-pole high-pass response by just 
subtracting a 4-pole low-pass response from the original input, is 
because of the phase-shift introduced by each stage.  You can use that 
simple approach for a 1st order filter, and even for a 2nd order filter 
with the right Q factor, but for higher order filters it gets more 
complicated.

-Richie,


On 2018-10-15 10:52, mark verbos wrote:
> 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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