An accurate measurement of parametric array using a spurious sound filter topologically equivalent to a half-wavelength resonator

Parametric arrays (PA) offer exceptional directivity and compactness compared to conventional loudspeakers, facilitating various acoustic applications. However, accurate measurement of audio signals generated by PA remains challenging due to spurious ultrasonic sounds arising from microphone nonlinearities. Existing filtering methods, including Helmholtz resonators, phononic crystals, polymer films, and grazing incidence techniques, exhibit practical constraints such as size limitations, fabrication complexity, or insufficient attenuation. To address these issues, we propose and demonstrate a novel acoustic filter based on the design of a half-wavelength resonator. The developed filter exploits the nodal plane in acoustic pressure distribution, effectively minimizing microphone exposure to targeted ultrasonic frequencies. Fabrication via stereolithography (SLA) 3D printing ensures high dimensional accuracy, which is crucial for high-frequency acoustic filters. Finite element method (FEM) simulations guided filter optimization for suppression frequencies at 40 kHz and 60 kHz, achieving high transmission loss (TL) around 60 dB. Experimental validations confirm the filter's superior performance in significantly reducing spurious acoustic signals, as reflected in frequency response, beam pattern, and propagation curve measurements. The proposed filter ensures stable and precise acoustic characterization, independent of measurement distances and incidence angles. This new approach not only improves measurement accuracy but also enhances reliability and reproducibility in parametric array research and development.

Gradient-Free Learning Based on the Kernel and the Range Space

In this article, we show that solving the system of linear equations by manipulating the kernel and the range space is equivalent to solving the problem of least squares error approximation. This establishes the ground for a gradient-free learning search when the system can be expressed in the form of a linear matrix equation. When the nonlinear activation function is invertible, the learning problem of a fully-connected multilayer feedforward neural network can be easily adapted for this novel learning framework. By a series of kernel and range space manipulations, it turns out that such a network learning boils down to solving a set of cross-coupling equations. By having the weights randomly initialized, the equations can be decoupled and the network solution shows relatively good learning capability for real world data sets of small to moderate dimensions. Based on the structural information of the matrix equation, the network representation is found to be dependent on the number of data samples and the output dimension.