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A linear filter for resolution of point sources

Linear, finite-impulse-response (FIR) filters are efficient for detecting point sources in data generated by a scanning detector array. In particular, matched filters have been widely used for detection and initial estimation of isolated sources. When separate sources have overlapping signals the matched filter does not work as well. Others have applied deconvolution filters to this case and shown good performance with high signal-to-noise ratios (SNR). The deconvolution filter is examined here in the context of general FIR filters. The novel aspect of this paper is the definition and application of an optimality concept for resolving arbitrary numbers of sources. A "resolution" attribute is defined which measures the difference between filter peak response and minimum response between adjacent peaks. A "max_min" filter is derived which has maximal resolution for given requirements on SNR and source separation distance. Its performance is compared with that of deconvolution.