The effect of DSP on the point spread function of a sonar beamformer

In order to characterise the performance of a sonar beamformer due to the digital signal processing algorithm, the analogy with a 1-dimensional temporal linear system is important. In essence, a 1D linear system can be characterised by its impulse response, h(t), and (by convolution) the response of the system, y(t), can be evaluated from the input, x(t). The beamformer analogy relies on the fact that a sonar beamformer (with a 1D array) is effectively a 2-dimensional linear system where the input X(x,y) is modified by the imaging system transfer function, H(x,y), to give a 2D image at the output, Y(x,y). The imaging system transfer function is its impulse response to X(x,y)=δ(x,y), or a point source. H(x,y) is also known as the point spread function (PSF), which can be expressed in any coordinate framework. The beamformer PSF can then be evaluated in simulation by considering the effect of varying parameters in the DSP/beamformer algorithm, and noting their effect. This work discusses the effect on the PSF of varying the most significant digital signal processing, parameters in the Heriot-Watt focused beamformer. An introduction to the hardware prototype demonstrator and future applications of this sonar is also presented