Multirate digital signal processing algorithm to calculate complex acoustic pressure fields

Abstract

An efficient algorithm to compute complex (magnitude and phase) acoustic pressure field data that uses a multirate digital processing architecture is presented. The algorithm is based on the discretization of the velocity potential function, sampled at a rate that varies as a function of field point location and transducer geometry. The algorithm can be used to determine accurate magnitude and phase information at any field point location, and for any transducer geometry with a closed-form velocity potential function, including planar pistons, spherically focused pistons, and planar annular array transducers (e.g., the nondiffracting or J0-Bessel transducer). Numerical simulations based on this algorithm are presented together with exact field calculations wherever possible in order to make absolute error comparisons. Additionally, results based on a standard Gaussian quadrature integration scheme are presented in order to compare computational speed and accuracy in the near field. Results indicate improvements in numerical efficiency of 15 to 30 times over standard numerical integration techniques.