A convolution model for computing the far-field directivity of a parametric loudspeaker array

Abstract

This paper describes a method to compute the far-field directivity of a parametric loudspeaker array (PLA), whereby the steerable parametric loudspeaker can be implemented when phased array techniques are applied. The convolution of the product directivity and the Westervelt's directivity is suggested, substituting for the past practice of using the product directivity only. Computed directivity of a PLA using the proposed convolution model achieves significant improvement in agreement to measured directivity at a negligible computational cost.

Generating dual beams from a single steerable parametric loudspeaker

“…Therefore, when the PFs are transmitted in one direction, the DF wave resultant from the parametric array effect is found to appear in the same direction. There is a recent development of the directivity model that adds a convolution operation with the Westervelt's directivity, which has been demonstrated to have a higher accuracy [5]. Therefore, this paper utilizes the new convolution model in all the simulations.…”

“…Furthermore, as a result of the absorption in air, the PFs, sum frequency, and higher order harmonics decay more rapidly than the DF [4]. More importantly, the DF is audible and still exhibits a narrow directivity pattern, which can be modeled by an end-fire array of virtual sources [2,5].…”

Construction of an Omnidirectional Parametric Loudspeaker Consisting in a Spherical Distribution of Ultrasound Transducers

“…The first step was to incorporate the product of the primary field directivities into Equation (4) (see, e.g., [31] and also [20,32] for a recent review on further approaches). Quite recently, a convolution model was developed to deal with PLAs whose PZTs could have beam widths up to 80∘ [33]. The model suggests the following prediction formula for the acoustic far field, (to be compared with Equation (4)), pd(r0,θ0)=Kcos(ωdt−kdr0)∫−ψ0ψ0D1(ψ)D2(ψ)DW(θ0−ψ)dψ.…”

Reproducing personal sound zones using a hybrid synthesis of dynamic and parametric loudspeakers

“…Earlier models include Westervelt's directivity (WD) [13] and product directivity (PD) [23], [24], though, these models do not accurately match measured directivity from a PL. Recently a convolutional directivity (CD) model, used in this work, was proposed [12], [25] utilising both WD and PD which has better correlation to measured directivity.…”

“…The CD is defined as the convolution between the PD and WD with the linear convolution operator, * , as [12], [25] (12) where k c is the ultrasonic carrier frequency, D G x,k is the Gaussian directivity [24] …”