Scaling method by using cubic-like triple point slop control...

Details Scaling method by using cubic-like triple point slop control... Scaling method by using cubic-like triple point slop control...

2006-12-05

2006-12-05

Mai, Tan V. (Department: 2193)

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

Reexamination Certificate

active

07146393

ABSTRACT:
A scaling method is to scale source data to destination data, wherein three reference points of the source data denoted as −1, 0, and 1. Function f(x)=ax2+bx+c are used to describe the destination data within 0 and 1. The method includes setting a midpoint 0.5 with a quantity of f(0.5)=[f(0)+f(1)]/2 and f′(0)=f′(1)=DG; wherein D is a slope of [2f(0)−f(−1)−f(1)], and G is a gain factor to adjust the slope. Curve f(x) passes through the points of 0, 0.5, and 1. The coefficients of a, b, and c for f(x) are solved by a range of 0≦x<0.5 and a range of 0.5≦x<1, so that the f(x) is symmetric or substantially symmetric to the midpoint Curve is set to have:in-line-formulae description="In-line Formulae" end="lead"?f(x)=2[f(1)−f(0)−DG]x2+(DG)x+f(0) for 0≦x<0.5; andin-line-formulae description="In-line Formulae" end="tail"?in-line-formulae description="In-line Formulae" end="lead"?f(x)=2[DG+f(0)−f(1)]x2+[4f(1)−4f(0)−3DG]x+[DG−f(1)+2f(0)] for 0.5≦x<1.in-line-formulae description="In-line Formulae" end="tail"?

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