Signal Resolution via Digital Inverse Filtering

Research in numerous areas is directed toward the resolution of multiple overlapping signals in a noisy environment. These areas include radar, sonar, speech, seismology, and electrophysiology. Sometimes matched filters are used; other times inverse filters are employed. This paper discusses one approach to the analysis of the resolution of inverse filters. Our method is to compromise the trade-off between signal resolution and the output signal-to-noise ratio (SNR). A performance measure for the inverse or deconvolution filter is defined as a quantity proportional to the harmonic mean of the resolution and the SNR. An optimum output pulse duration is obtained using this criterion, where the pulse shape has been previously selected and the input signal waveform is known. In addition, upper and lower bounds for the output pulse duration are presented. Graphs are given which allow the designer to select the optimum inverse filter output pulse duration for a desired signal resolution and an estimated SNR.