This thesis is concerned with the estimation of the acoustic source signal-bearing in the presence of a reflective surface. The method to estimate the bearing of the acoustic source is the cross spectral analysis of two microphones in which the characteristics of the acoustic source signal is preserved. The echo of the original time history is removed by an advanced signal processing technique, called Cepstrum analysis. This technique is successfully applied to remove the contaminating effect of echoes in the measured time history. The work described is divided into several steps. A computer program was developed to examine the effects of reflection and the behavior of the Cepstrum under different operating conditions using simulated signals. The algorithm was then adapted to process experimental signals acquired under laboratory test conditions. An improved liftering process based on the knowledge of the echo time was developed in order to make the method relatively automated. The results of the experimental work show that the Cepstral analysis can be both effective and efficient in removing reflected signals from convolved time histories and thus successful in correcting a bearing estimate contaminated by an echo. / M.S.