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Data Link Error Detection / Correction Methods

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Scott Dattalo

How to measure linearity error.

1) Collect a whole bunch of data and record a) the voltage applied and b) and the converted digital value. You also should collect several samples at each voltage value and use the mean of the digital values to represent converted digital value. There's another test for measuring the spread.

2) Find the least square's curve fit of the data. In other words, find the line that best fits the data.

3) Find the sample that most deviates from this line.

The line found by the least square's curve fit is of the form: 

   y = m*x + b

where
 x = true value of the input signal (the applied voltage)

 y = expected value when the true value is applied (the actual value is
     what you measure)

 m & b are the slope and intercept of the line and are calculated:


m = [s(x) * s(x * d) - s(x*x) s(d)] / den

b = [s(x) * s(d) - n * s(x * d) ] / den

den = s(x)*s(x) - n * s(x*x)

where,

d = digitized value
n = total number of samples

and
          n
        -----
        \
s( ) =  /     (   )
        -----
         i=1

Once you have m and b, you can perform step 3 by running the applied voltage through the line representing the data and comparing the expected value output with the value you actually measured. The Linearity Error is then: 


L = max( ( d - y ) / x_fr ) * 100%

where x_fr is the full range of the data, or 4096 for a 12-bit A/D.

Like I said earlier, I've got an octave program to do this. If anyone wants it, drop me a line. You probably can find a lsf function in excel too.

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file: /techref/method/errors.htm, 8KB, , updated: 2008/8/28 15:25, local time: 2008/9/4 21:50,
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