1. A method for extracting intermittent, randomly occurring transient target signals of known type from a raw data source signal containing an unknown number of the target signals in addition to interfering signals or intrinsic noise signals, the method comprising: a) defining quantifiable signatures or characteristics that respectively and independently represent the target signals, the interfering signals or the intrinsic noise signals; b) transforming the raw data source signal with a mathematical transform that effects a decomposition of the source signal into distinct data sets; c) processing said data sets to identify a first group of data sets which display the signatures or characteristics representing the interfering signals or intrinsic noise signals and a second group of data sets which display the signatures or characteristics representing the target signals; d) setting the data sets of the first group to zero; and e) applying an inverse transform to the processed data sets in order to reconstruct a processed output signal.