Multirate digital signal processing algorithm to calculate complex acoustic pressure fields

Donald P. Orofino, Peder C. Pedersen
1992 Journal of the Acoustical Society of America  
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
more » ... ity potential function, including planar pistons, spherically focused pistons, and planar annular array transducers (e.g., the nondiffracting or Jo-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. PACS numbers: 43.20.Rz, 43.40.Le, 43.35.Ze LIST OF SYMBOLS h [ n ] a transducer radius, or projected radius for spheri-haa (r,t) cally focused piston outer radius of ith ring of annular transducer speed of propagation in medium depth of spherically focused transducer envelope of magnitude spectrum of velocity potential function at axial field points, for a given transducer geometry Fourier transform of quantity fast Fourier transform frequency, Hertz upper limit of desired baseband frequency range Nyquist frequency, = f•/2 Nyquist frequency after ith stage of decimation, i= 1,2 Nyquist frequency after decimation, e.g., 563 J. Acoust. Soc. Am. 92 (1),
doi:10.1121/1.404265 fatcat:sm6ne4xq6bd4pda72advksragm