On Mon, Aug 25, 2008 at 7:48 AM, PSPunch shima@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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