Optimized constant beam width arrays

Abstract

It has been previously shown by the authors [JAES 34, 221 (April 1990); J. Acoust. Soc. Am. 91, 2326 (A) (1992)] that the main beamwidth of a loudspeaker array can be held constant over an octave by the superposition of two arrays by using suitable filter functions. The beam patterns are identical at the end (design) frequencies, however, deviations occur at frequencies between the extremes. The deviations are representative of unwanted acoustic energy if the deviation is positive when referenced to the desired pattern. While the array has some error at these design frequencies (for example, undesired side and backlobes), the total error energy integrated over the octave may be greater than that of other arrays that use element weights that allow more error at the design frequencies. Presented is an algorithm to minimize the deviations between design frequencies while minimizing the error energies, which is based on a Wiener adaptation. The results are compared to hand-generated guesses. The impact of linear and nonlinear cost functions is considered.