Chebby shev ..math head needed

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gentleclockdivider
gentleclockdivider Member Posts: 364 Advisor
edited October 2024 in Reaktor

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

2.jpg


I implemented this is reaktor like this

1.jpg

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.

3.jpg


Comments

  • Bryn Owen
    Bryn Owen Member Posts: 23 Member

    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
    Ari_BirthdaySurprise Member Posts: 6 Member

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

  • PoorFellow
    PoorFellow Moderator Posts: 7,381 mod

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

  • Kubrak
    Kubrak Member Posts: 3,154 Expert

    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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