# Why Digitize Data?

• Interpolation and extrapolation

Suppose you have obtained a set of digital data and plotted a working curve. If you make a fresh measurement on a fresh sample, can you use the working curve to measure the behavior of that sample? Usually, the answer is: if the new data fall within the range of the working curve so that one interpolates, one can trust the new data, but if the new data fall outside the previously validated range, one can not trust the use of the curve. Certainly distrusting extrapolation is appropriate for digitized as well as continuous (analog) data. But is interpolation within the range of a working curve always justified? With sufficient signal averaging so that there are sufficient significant figures, the answer is yes, but for sufficiently low noise systems, the granularity of digitization poses a problem. Since all digitization is inherently an integer process, there will be jumps in the measurement output as the digitized value increments by one count at a time. This is stairstepping.

• Stair-stepping

As we vary a continuous variable, typically electrical potential, and digitize the value, we get a response that, in the absence of noise, looks like this:

 The horizontal red and blue lines show two integer values that can represent potential. If the potential is actually that indicated by the vertical green line, then what? Either the blue or red number will appear, giving no indication that
the actual number should be half-way in between! Only if there is noise, so that the instantaneous value jumps back and forth between the red and blue levels can we signal average to get a fractional number that would allow interpolation!