Transducer Array Directional Frequency Response Analysis
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Solution Overview
Problem
Existing methods for determining the directional frequency response of sensor arrays are time-consuming, inconvenient, and costly, especially when comparing multiple arrays or for applications like radio astronomy where arrays span several kilometers.
Innovation Solution
A computer-implemented method that converts a simulation of transducer element locations from the spatial domain to the spatial frequency domain, allowing for the determination of directional frequency response across a wide frequency band with a single transformation, and translating this into a modified frequency domain for specific beamforming directions and frequency ranges.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If time domain simulation methods are used to determine directional frequency response, then measurement accuracy is improved, but execution time increases appreciably with the number of frequencies simulated
Solution Approach 1:
The patent replaces time domain simulation methods with a spatial frequency domain approach using Fourier transforms. Instead of simulating wave propagation in the time domain for each frequency, the method uses spatial Fourier transforms of the array geometry to directly compute frequency response, substituting a mathematical transformation for computational simulation.
Solution Approach 2:
The patent changes the domain of computation from time domain to spatial frequency domain. By transforming the problem into the spatial frequency domain using Fourier transforms, the method computes directional frequency response for multiple frequencies simultaneously rather than sequentially, fundamentally changing how the parameter is calculated.
2Reliability
If physical array construction is performed to measure directional frequency response, then measurement reliability is improved, but cost and convenience deteriorate
Solution Approach 1:
The patent creates a mathematical model (copy) of the physical array geometry and uses spatial Fourier transforms to compute the directional frequency response from this model. This virtual copy allows prediction of array performance without constructing the physical array, eliminating the need for expensive and time-consuming physical prototypes.
3Adaptability or versatility
If directional frequency response is determined for multiple frequencies using conventional methods, then frequency coverage is improved, but computational complexity increases
Solution Approach 1:
The patent creates a universal computational approach where a single spatial Fourier transform of the array geometry provides the directional frequency response for all frequencies simultaneously. This multi-functional method replaces multiple frequency-specific simulations with one transformation that covers the entire frequency spectrum.
Data Source
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AI summary
A method for determining the directional frequency response of an arrangement of transducer elements. The method comprises providing a simulation of locations of the transducer elements, in the spatial domain; providing a beamforming direction and a frequency range; converting the simulation of locations from the spatial domain into corresponding frequency response values in a spatial frequency domain, such that, for each frequency of a plurality of frequencies in the frequency range, a spatial frequency contour is defined, each of the spatial frequency contours intersecting at the origin; determining the frequency response by applying a transformation to the frequency response values for the provided beamforming direction and frequency range, translating the spatial frequency domain into a modified frequency domain, wherein the contours avoid intersecting; and outputting the frequency response. There is further provided a data processing device adapted to perform the method, a computer program, and a computer-readable medium.