Partitioned and Linearly Approximated Impulse Responses for Rapid Calculation of Radiated Sound Fields from Rectangular Transducers

A rapid calculation method for the radiated sound field from a rectangular transducer is proposed. The radiated field is calculated using the convolution integral between the driving signal of the transducer and the time derivative of the spatial impulse response. The proposed method partitions the integral interval with the driving signal of the transducer and approximates the spatial impulse response as a straight line. The time derivative of the response takes constant values. These constant values are separately multiplied by integrated values of the driving signal prepared in advance. The convolution integral is expressed in a very brief form using several basic mathematical operations. Therefore, the time required for the entire calculation is markedly reduced. It becomes at least about 1/40 of that in which the convolution is directly calculated using the conventional method.