3E-2 A Curve Fitting Approach for Fast Calculations of Spatial Impulse Responses

A new approach for calculating approximations of spatial impulse responses (SIRs) of transducers of arbitrary shape is proposed. It is based on the observation that SIRs of most practical transducer shapes can be well described as piecewise smooth functions which can be well approximated by standard function approximation tools. In this paper, discrete orthogonal Legendre polynomials are used as base functions in the approximation. A two-stage approach is used. In the first stage, SIRs for a set of training points are calculated using numerical techniques and polynomial coefficients are extracted for the segments in these SIRs. The curve shapes of the segments of SIRs for arbitrary observation points are recovered using polynomial coefficients that are interpolated from coefficients of corresponding segments in the training set. The SIRs calculated using the method show good agreement with those obtained from numerical integration and the calculation time can, depending on the geometry of the transducer, be reduced significantly