Importance of Curve Fitting
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Abstract
Importance of Curve Fitting
Curve fitting data to a continuous math function is commonly done for the following reasons:
- interpolation and/or extrapolation of data;
- parameter estimation where derivative values are required;
- ease to ‘picture’ a technical problem in publications, seminars, & conferences; and,
- verifying micro-chip manufacturing processes and building of chips.
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Figure.1.1 A perfect model to Odd data |
The last is relatively new and few are aware of the practice. But, while working at Memorex in the 1980s, my manager asked for a math model of an isolated pulse from reading a disc drive. A pulse model was created and used to test other circuit designs and ideas. I was given 200 disc drives to test how well the math model worked overall. 199 discs agreed pretty well to a pulse similar to that show in figure 1.2 below. But number 200, showed something never seem before; see figure 1.1. Our math model fit even this dataset well! This convinced us that the model was excellent. After thinking about this odd curve and talking amongst our selves, we concluded that the chip was defective. This finding was pointed out to the manufacturing department who were looking for a way to detect bad chips. 
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