Abstract: The present invention relates to the method to identify the source of a signature signal by processing sparse digital data collected by a sensor system in a laboratory, field, or other application. The invention specifically addresses weak, obscured, or partially sampled signatures collected by a sensor system. The method takes advantage of all sources of data using an innovative method that uses Bayes Theorem for performing probability arithmetic and statistical inference. The method requires an exclusive and exhaustive library of candidate signatures. The method finds the most likely signature candidate from the library that has the highest likelihood of being responsible for the measured signal. In addition, the method can work with mixtures of library candidates to find the most likely mixture that explain the data. The method is applicable to a variety of sensor systems that collect and digitize data as signal strength (ordinate) versus measurement attribute (abscissa).