Time domain signal transmission and source location in a waveguide: matched filter and deconvolution experiments

The experiments were made in an ideal air waveguide having Sheetrock (hard) boundaries. Transmissions of a signal were from a source to a pair of receivers. Matched filter and deconvolution procedures were tested. Matched filters were computed for transmissions from a set of trial source locations to the receivers. The trial matched filters were then applied to the signals. The filtered signals were cross correlated. A map of cross-correlation absolute maxima for trial source locations gave the actual source location. Many smaller maxima indicated false locations. For the second method, the signals were deconvolved with estimates of the impulse transmission from trial locations. At the actual source location, deconvolution operations gave a diverging oscillatory remainder. The oscillations had a higher frequency than the signal. It was possible to low-pass filter the deconvolved signals and recover good replicas of the transmitted signal. The map of cross correlations of the deconvolved and filtered signals gave the source location. The deconvolution–low-pass filter method gave fewer and smaller indications of false locations than the matched filter method. However, the matched filter method was more tolerant of errors in the estimates of the impulse response.