[PD] Avoiding clipping with tabread4

[Charles Henry]

On Mon, Aug 25, 2008 at 7:48 AM, PSPunch <shima at pspunch.com> wrote:
> i.e., having a table of [-1 1 1 -1], an index of 1.5 will return 1.25
> with [tabread4]

This is correct.  The interpolated values can exceed the values in the
samples.  Think about drawing a polynomial through your points, and
where the maximum actually can occur.

> Are there any common practices to avoid unexpected clipping introduced
> by [tabread4] or [tabosc4~] ?

Common practices, not sure.  But I think we can establish an upper
bound on the peak value, analytically.

Our polynomial for tabread4~:

g(x)=
   f[-1]*x(x-1)(x-2)/-6
+ f[0]*(x+1)(x-1)(x-2)/2
+ f[1]*(x+1)x(x-2)/-2
+ f[2]*(x+1)x(x-1)/6

So, the maximum value must occur as a function of x between 0 and 1.
Taking our input peak value as 1, the maximum output peak is the sum
of the absolute value of the coefficients of f[-1], f[0], f[1], f[2]

x(x-1)(x-2)/6 + (x+1)(x-1)(x-2)/2 - (x+1)x(x-2)/2 - (x+1)x(x-1)/6

= -x^2 + x + 1

vertex:  x=1/2, f(1/2) = 1.25

> Further more, under what circumstances (what 4 values referred to) will
> the returned value exceed the range most?

How do you like answering your own questions :)  Your example is exactly it.

Chuck

>
>
> Thanks in advance..
>
> --
> David Shimamoto
>
>
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