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Recovering errors?



Anything is more plesant than grading. The first two columns show very
good data representing the y=x^n function. Column 3 shows what happens
to these "data" when hardware is not good. In this case it is a simple
truncation (as it might happen in an analog-to-digital convertor). How
accurately can the original n=2 be recognized by performing the least-
square analysis of the distorted y2 data? My guess is that the answer
depends on the total number of data points. For a lot of points the
recovered n will be very close to 2. This shows that software can
overcome limitations of hardware, sometimes. Can this be done on the
falling ball data which were discussed in another thread?

Ludwik Kowalski
P.S.
The function has to be monitonic. Otherwise the information lost may
not be recoverable.

x y1 y2

2.00 4.000 4.0
2.02 4.080 4.0
2.04 4.162 4.1
2.06 4.244 4.2
......
3.96 15.68 15.6
3.98 15.84 15.8
4.00 16.00 16.0