Experiments with echo detection in the presence of noise using the power cepstrum and a modification

The power cepstrum of a function is found by computing the power spectrum of the logarithm of the power spectrum of that function. In addition, some applications of the cepstrum employ a smoothing (windowing) function immediately before or after the logarithm operation. This paper describes some experiments in echo-time detection and quefrency-band power measurements performed on ultrasound waveforms, both by the standard cepstral method and by the deletion of either or both of the window and the logarithm from that method. It is shown that echo-time detection in the presence of noise is achieved more reliably without the logarithm step for the waveforms of interest. Our experimental findings compare favorably with theoretical results reported recently by Hassab and Boucher [2].