Ziqiang Hu and J. Stuart Bolton, "The Use of the Fast Hankel Transform for Sound Radiation Calculations with Application to the Prediction of Sound Radiation from an Arbitrarily Positioned Multipole Placed Near a Plane Reflecting Surface," unpublished manuscript prepared for the Journal of Sound and Vibration, 33 pages, 9 figures, 7 tables (1992).


In a recent paper the authors described the use of a finite, two-dimensional discrete Hankel transform to predict the sound radiation from multipole sources placed near reflecting surfaces. When using that technique, the wavenumber spectrum of the incident sound field is first defined either numerically or analytically. The incident wavenumber spectrum is then combined with the reflection coefficient of the surface to yield the wavenumber spectrum of the reflected field which can then be added to the incident field and the result inverse transformed to give the spatial distribution of the sound pressure. In principle that technique may be used to predict the sound radiation from arbitrarily directional sources. However, owing to the time required to evaluate the inverse Hankel transform directly in discrete form, the calculation of a spatial sound pressure distribution can be time consuming if the source is of high order: i.e., if its sound field comprises a large number of azimuthally harmonic components. Thus in this paper the performance of a Fast Hankel Transform (FHT) algorithm when applied to sound propagation predictions is compared with that of a direct evaluation of the inverse Discrete Hankel Transform (DHT). The use of a previously proposed FHT has been investigated and its performance was compared to that of the DHT by considering the product of the mean square prediction error and the required computation time. The FHT in its original form was found to be "noisy", thus diminishing its advantage with respect to the DHT, especially for large transform lengths. In this paper it will be shown that a simple modification to the FHT algorithm can under some circumstances result in improved prediction accuracy without a substantial increase in computation time. Thus it is concluded that the use of the FHT rather than the DHT can usually yield a significant reduction in the computation time required to make propagation predictions to a specified level of accuracy. As an example of the use of the FHT, a calculation is presented in which the sound propagation from a multipole source displaced from the radial origin of a cylindrical coordinate system is considered. In that case, an infinite number of terms is strictly required in the cylindrically harmonic expansion of the sound field. However, here it is shown that the cylindrically harmonic expansion of the sound field may be truncated after a finite number of terms with the result that accurate predictions may be made without undue computation time.


Fast Hankel Transform, Multipole sound field, Propagation prediction, Reflecting surfaces


Acoustics and Noise Control

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