Sound Field Reconstruction Using Wave Function Interpolation
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Solution Overview
Problem
Existing Near-field Acoustical Holography methods face challenges such as severe spatial windowing effects, increased complexity, and computational demands, especially when the measurement area does not fully cover regions with high sound pressure, and previous methods like HELS introduce errors when the sound source surface is not spherical and require a large number of measurement positions.
Innovation Solution
A method that computes correlation functions indicative of plane propagating and evanescent waves, using interpolation functions to efficiently reconstruct the sound field, allowing for general geometries and various acoustical quantities, with stored interpolation functions requiring minimal storage capacity and enabling faster computation by approximately a factor of 10 compared to prior art.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If spatial DFT is used for NAH calculation, then processing speed is improved, but spatial windowing effects increase severely
Solution Approach 1:
The patent replaces the traditional spatial DFT mechanical processing system with a wave function expansion system. Instead of using discrete Fourier transforms on grid measurements, the invention uses continuous wave functions (spherical, cylindrical, or plane waves) to represent the acoustic field, allowing for more flexible and accurate field reconstruction without severe windowing effects.
Solution Approach 2:
The patent changes the fundamental parameters of the NAH calculation by transitioning from discrete spatial frequency domain (DFT) to continuous wave function domain. This parameter change allows the measurement area to be smaller while maintaining accuracy, as the wave function expansion can extrapolate the field behavior beyond the measured region.
2Area of stationary object
If HELS method with spherical wave functions is used, then measurement area requirement is reduced, but errors are introduced when source surface is not spherical
Solution Approach 1:
The patent creates a universal NAH method that can handle various source geometries (spherical, cylindrical, planar, or arbitrary shapes) by providing multiple wave function expansion options. The user can select the appropriate wave function type based on the source geometry, making the method universally applicable while maintaining accuracy for each specific case.
Solution Approach 2:
The patent combines multiple wave function types (spherical, cylindrical, plane waves) into a composite expansion framework. This allows the method to adapt to different source geometries by selecting or combining appropriate wave function components, similar to how composite materials combine different material properties to achieve desired characteristics.
3Device complexity
If HELS method is used without proper scaling, then wave function representation is simplified, but regularization methods fail to work properly
Solution Approach 1:
The patent introduces proper scaling of wave function parameters to ensure that regularization methods can effectively control the ill-posed nature of the inverse problem. By appropriately scaling the wave function amplitudes and phases, the method maintains numerical stability while preserving the simplicity of the wave function representation.
4Measurement precision
If iterative search for optimal truncation is used, then solution accuracy is improved, but computational cost increases significantly
Solution Approach 1:
The patent performs preliminary determination of the optimal number of wave function terms based on the measurement geometry and frequency range before the actual reconstruction. This preliminary action avoids the need for iterative search during the reconstruction process, significantly reducing computational cost while maintaining solution accuracy.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This method provides accurate and computationally efficient sound field reconstruction for arbitrary sound sources and geometries, reducing errors and computational complexity, while allowing for faster processing and improved spatial resolution.
Implementation Method 1
computing each of a set of correlation functions, each correlation function being indicative of a correlation of at least one set of plane propagating and evanescent waves at a first one of said measurement locations with the at least one set of plane waves at a second location
Implementation Method 2
computing each of a set of correlation functions, each correlation function being indicative of a correlation of at least one set of plane propagating and evanescent waves
Data Source
AI summary
Disclosed is a method of reconstructing a sound field. The method comprises receiving measured values of a first acoustic quantity measured at a set of measurement locations; computing a second acoustic quantity for a target location from a superposition of plane waves. The method comprises storing a set of representations of interpolations of respective functions, each function being a function of two or less input parameters; and computing comprises computing each of a set of correlation functions, each correlation function being indicative of a correlation of the plane waves at a first one of said measurement locations with the plane waves at a second location, as a linear combination of values obtained from the set of representations of interpolations.