[sdiy] Oberheim Xpander Multimode VCF Question

[Magnus Danielson]

Steven Cook wrote:
> Hi,
> 
> Is it possible to get a -24dB/oct allpass response out of an Oberheim 
> Xpander type of 4-pole filter arrangement? I've got the following for an 
> -18dB allpass, from a post by David G. Dixon...
> 
> input + pole1*3 - pole2*6 + pole3*4
> 
> Which seems to work fine (in software).

I'm in a hurry, so you will not get the complete answer now... from me 
at least.

First of all, you can't talk about -24 dB/Oct slope for an all-pass 
filter. While I am happy that you say -24 dB/Oct for low-pass, it is 
meaningless for all-pass as they are 0 dB/Oct. This only once again 
brings out the point... the slope does not tell how many poles and zeros 
there is in a filter, just how many there at least needs to be.

Now, the actual question is, can you create a 4-pole/4-zero all-pass 
filter from the Xpander module? The quick answer is yes.

What I don't have time to help you with is how to combine the outputs 
from the different taps, but you are on the right path when you combine 
input with the taps.

For non-complex poles, you have (s+a)/(s-a) for each stage. For complex 
poles (s+a-jb)(s+a+jb)/(s-a-jb)/(s-a+jb). Notice how the real term a 
shift sign from poles to zero. Any all-pass filter is then just a 
combination of those using various sets of a and b. You should be able 
to pull it out from there with some paper-and-pen work, which is the 
thing I don't have time for right now.

If you still have problem, let me know. I might be able to do the 
homework for you later.

Cheers,
Magnus