Optimum time domain signal transmission and source location in a waveguide: Experiments in an ideal wedge waveguide

Abstract

Source location experiments in a wedge waveguide were conducted to test a single-channel time domain technique for a known source. The laboratory measurements were made in the air wedge having rigid sheet rock boundaries. The wedge angle was 6.6°. The source transmitted a short oscillatory signal having a frequency band of 3–13 kHz. The distances of the source and receiver from the wedge apex were 1.85 and 3.13 m. The Biot–Tolstoy wedge solution was used to calculate the source-to-receiver impulse response. For the geometry, all of the arrivals are due to images. The waveguide matched filter was the time reverse of the theoretical impulse response. The output of the matched filter was cross correlated with the known input signal. Maps of possible source locations were made by (i) assuming a trial source location, (ii) computing a theoretical impulse response and the corresponding matched filter, (iii) filtering the signal, and (iv) mapping the peak absolute maximum of the matched filter output. The actual source location was correctly mapped. There were several lower amplitude maxima that gave false source locations. The Appendix includes a tutorial description of the Laplace generating function (z transforms) and their applications.