Chebby shev ..math head needed

gentleclockdivider · 2024-02-27T00:01:25+00:00

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gentleclockdivider

A coupleof years ago I made a shaper with used the first 10 chebby polynomials

It worked great and correctly , since a 0db sine wave as input give all the overtones for each polynomial .

BUt , I am having someserious brain fart issues

Take this chebby shev one

4x^3 - 3x

I implemented this is reaktor like this

Which I think is correct ..

The input signal is cubed , then mulitplied by 4 , and eventualy the signal mutiplied by 3 is subtracted from it .

Let's focus on the first portion , should the cubed input sig be mutiplied by 4 , or should the input sig be multied by 4 and then cubed ?

Two different things , as seen here in pure data

edit .the input signal in the pure data patch is a ramp going from 0 to 1 over 512 index points

It's not real time audio , but a pure recursive calculation writing the formula in table .

There is an obvious difference whether the input signal is first Cubed then multie by 4 (bluebox ) compared to (4*sig)^3

It's impossible that my reaktor implementation is wrong since it bahaves as chebby poly should behave.

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Comments

Bryn Owen

This is very cool! I can tell you from the math side, you have done it correctly in your first Reaktor block diagram, and I think in the blue box. 4x^3 means cube the signal, then multiply that result by 4. It does not mean (4x)^3 so the red box would not be correct.

Ari_BirthdaySurprise

What Bryn said. Great job making this despite not fully understanding the math!

PoorFellow

For that kind of Reaktor stuff you most likely needs Reaktor expert colb

Kubrak

As others said, first comes power, the multiplication follows next.... Vice versa would be false, it would be 4^3*x^3, so 48x^3, not 4x^3.

I have no Reaktor experience, but what comes to my mind, wouldn't it be CPU more effective if you use multiplication instead power.

x^2 is x*x

x^3 is x*x^2 (you would use x^2 result from previous line)

x^4 is x*x^3 (you would use x^3 result from previous line)

So, instead of four times using power to (CPU intensive), three multiplications (CPU easy) would do the same.

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