Application of the Fourier series method to the detecton and localization of signals embedded in a noise background

A Fourier series technique to enhance signal‐to‐noise ratio and to estimate the azimuth of signals embedded in a noise background is developed in this paper. The method uses beam measurements made by horizontal line array as inputs. Currently, the average value of incoming energy across a given beam is utilized directly or empirically to estimate the arrival intensity and azimuth. Dividing the beam energy by the beamwidth produces an estimate that is the average of signal times array beam pattern function. The average value of energy from a single source is considerably lower than the corresponding peak value. Also, the azimuth of an incoming signal of interest must be estimated empirically from average intensity levels at adjacent beam centers. The primary objective of this analysis is to provide an estimate of peak values (rather than average values) of the acoustic energy at all azimuths by applying the Fourier series method to utilize the full beam pattern of the array. In the method described in this paper, the acoustic field is expanded in a Fourier series and Fourier coefficients are determined from beam intensity measurements. The method provides a best estimation of the signal plus noise field from beam measurements of a line array system, since the Fourier series is a trigonometric polynomial with the smallest mean square difference from the actual horizontal noise field. The major conclusion of this analysis is that signal‐to‐noise ratio and estimation of the azimuth of distant signals measured by line array systems are enhanced when the Fourier series method is applied to beam measurements. Enhancement results in the improved prediction of (1) signal arrival azimuth and (2) peak signal level. These conclusions are based on application of the Fourier series method to a limited number of mathematical models of acoustic fields; further evaluation of the Fourier series method for a greater variety of mathematical model acoustic fields is necessary to further quantify the results.