Droop Correction

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It is very easy to correct a digitized signal for droop:

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 Often, a measured signal, V1, will have a droop associated with an RC or L/R decay time.  This is equivalent to the desired signal, V0, being sent through a high-pass RC filter before being recorded:

         where, 

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To get the desired signal back, we need to multiply by the inverse of the high-pass RC filter transfer function and generate a droop corrected signal, V2:

 

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So, the correction in the frequency domain, H(ω), is:

 

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Because of the linearity of the Fourier transform and recognizing that division by jω in the frequency domain is integration in the time domain:

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So, it turns out that this correction is nearly trivial to make with a computer code:

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For (i=0; i<NumberOfPoints; i++)

{

    Integral+=v1[i]*TimeStep;

    v2[i]=v1[i]+Integral/RC;

 };

    Raymond Allen 2006