# 4PM no HP4 mode?

Hello everyone - I’m new here!

I signed in just to ask - is there any technical reason why 4 Pole Mission doesn’t have a 4 pole highpass filter mode? I’m just curious.

Thanks for the info. Cheers!

you’re not THE EvilDragon aren’t you?
(guess I have won the derail thread at first post compo haven’t I?)
anyway, I don’t have an answer to your question…

If by “THE EvilDragon” you mean that EvilDragon from Reaper, Harmony Central, Gearslutz, KvR, Native Instruments, and some other forums… then yes, I am THAT EvilDragon.

By mixing the 4 outputs of a 4-pole cascade, you can achieve any transfer function that can be decomposed as :

a / (1 + s) + b / (1 + s) ^ 2 + c / (1 + s) ^ 3 + d / (1 + s) ^ 4

If you compute this sum (sum everything to the lowest common denominator, ie (1 + s) ^ 4), the numerator will be a 3rd degree polynomial. So pole-mixing can achieve any transfer function with a 3rd degree polynomial as a numerator, and (1 + s) ^ 4 as a denominator. Sadly, this does not include the 4-pole HP (TF: s ^ 4 / (1 + s) ^ 4), since the numerator is s ^ 4, 4th degree.

You can reach a different family of transfer functions by replacing an integrator in the chain by a unity gain. In this case, you can achieve any transfer function that can be decomposed as :

a + b / (1 + s) + c / (1 + s) ^ 2 + d / (1 + s) ^ 3

If you compute the sum, you can see that you can get any transfer function with a 3-rd degree polynomial as a numerator, and (1 + s) ^ 3 as the denominator. This includes a 3-pole HP (s ^ 3 / (1 + s) ^ 3), but not a 4-pole HP.

I have never been a big fan of the “get the HP mode by subtracting the LP output to the original signal” (broken for resonant filters - it’s an entirely different beast from s ^ 4 / (1 + s) ^ 4 since you get terms in s ^ 3, s ^ 2 and s in the numerator !). If I had to design a 4-pole HP I would do it with a cascade of 2 SVF like on the Jupiter-6…

Olivier, that is the best answer I have seen on this forum so far. Wish I understood it. Welcome EvilDragon!

Well, those DSP classes, Fourier transforms and calculus in s-plane have definitely paid off I understood your reply perfectly, pichenettes, thank you! So, it seems like I’m going to have to get 4PM and Dual SVF Shruthis, haha.

I can personally vouch for the granditude of the Dual-SVF. You won’t be disappointed!

@EvilDragon oh no then you’re not the one I was thinking of… anyway, welcome to the forums! Be the Shruthiness with you!

@rumplefilter: lol