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FDC2214: Derivation Integration Algorithm. Mathematical Basis.

MICHEL LE PIMPEC
Prodigy 60 points

Part Number: FDC2214

Hi,

I am using the FDC2214 for detecting fingers approaching to a target.
I will have to cope with temperature and humidity variations with some influence on the baseline. 

I have discoverd the Derivation Integration Algorithm (SNOA939) which looks well adapted for addressing these issues.
However, Il would like to understand the underlaying theory which leads to this algorithm, not only the algorithm.
Would you  know some appropriate references (TI, academic or others) ?

Thank you for your help

Michel LE PIMPEC / KELTELEC

,

 

  • 0
    TI__Expert 3450 points

    Hi Michel, 

    I am happy to have a brief discussion here about the reasoning behind this algorithm. 

    As you have seen in SNOA939, the premise is that tracking the change in subsequent data points (when above DT) from the FDC device by summing these changes, and comparing them to a threshold value will provide an reasonable indicator of object proximity as the baseline value changes. 

    The decay or leakage factor 'L' is utilized when the the summation of derivatives (referred to as the integral), is below the integral detection threshold. In this case the integral value is adjusted according to the geometric sequence a*(r^n), a = current integral value, r = L (leakage factor), and n is the number of subsequent times that the integral value is below the integral threshold. This is adjusted based on the needs of the application. The DT threshold adjusts how sensitive the integral is to a change in the sensor data. 

    The averaging filter option acts as a low pass filter applied to the sensor data, improving the SNR, and algorithm stability, but will decrease the accuracy depending on the number of data points or N value used. 

    This algorithm was created with easy implementation, minimal MCU utilization, and tunability in mind. 

    Regards,

    Gabriel

  • 0 in reply to Gabriel Lake1
    Prodigy 60 points

    Hi Gabriel,

    Many thanks for your answer. It clarifies the SNOA939 algorithm.

    However this looks quite empirical.
    I would like to understand from where it comes from a mathematical / signal theory / circuit theory point of view.

    Would you have any reference where this is explained ?

    Best regards

    Michel

  • 0 in reply to MICHEL LE PIMPEC
    TI__Expert 3450 points

    Hi Michel,

    While this algorithm is tailored to this type of application, as the app note mentioned, there are variations on this technique that are widely implemented in different sensor applications. It is beyond the scope of this forum to provide a detailed mathematical explanation of this class of sensor data processing. 

    The author drew from his signal processing knowledge and experience with this capacitive sensor to determine an adequate method for prototyping applications. Properties of derivatives, digital averaging filters, basics of numerical computing are three areas I recommend conducting your own research on, to gain a better understanding of the foundation of this algorithm's approach and its limitations. 

    Regards,

    Gabriel

     

  • 0 in reply to Gabriel Lake1
    Prodigy 60 points

    Hi Gabriel,

    Thank you for your answer.

    I will find the appropriate litterature by myself.

    Best regards

    Michel