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Usually we use Taylor series expansion while taking just the first few terms in the process of linearizing a nonlinear data of sensor recordings. However, another method exists which involves A/D conversion in particular as a discretization. I wish to understand how this operation transforms the non-linear data to a linear one.

The only reference I have in my course notes is the following statement

The result of the A/D conversion is used as an index into an array that stores the corrected data points.

SPARSE
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    It doesn't. The linearisation happens somewhere else, such as in processing the (sampled, quantized) signals. –  May 08 '22 at 11:20

1 Answers1

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Assuming a 16 bits ADC, you have \$2^{16} = 65536\$ possible numbers. Instead of linearly mapping these numbers to a value range (e. g. 0.0 to 5.0 V) you build a Look-Up Table with 65536 entries and use the ADC code to access this table. This way you get whatever non-linear mapping you need.

Hypothetical example of logarithmic LUT for a 4 bits ADC:

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Obviously it gets harder for a higher number of bits or embedded systems. What you can do as a compromise is not store every possible code, but do a Piecewise Linear approximation, by storing the intersection points of several linear segments and using the most significant bits to access them (and interpolate between them using the least significant bits).

devnull
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  • Consider using a LUT with 2^n entries, for examble 256. This way, you get away with bit operations to do the look-up procedure, which is very efficient. – Sim Son May 08 '22 at 13:43