Fourier Wavenumber Beamforming Without Interpolation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current digital beamforming methods require approximate interpolations, leading to low accuracy and longer processing times, especially when dealing with arbitrary aperture geometries and multidimensional arrays, which limits high-speed and high-accuracy beamforming for applications like medical ultrasound and communication systems.
Innovation Solution
The method employs Fourier's transform and wavenumber matching without approximate interpolations, using complex exponential functions and Jacobi operations to perform beamforming on arbitrary orthogonal coordinate systems, enabling high-speed and high-accuracy processing for arbitrary beamformings, including dynamic focusing and steering.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If approximate interpolation methods are used for wavenumber matching in digital beamforming, then processing can be simplified, but measurement precision and processing speed deteriorate
Solution Approach 1:
The patent replaces approximate mechanical interpolation methods with exact analytical wavenumber matching using Fourier transforms and complex exponential functions. This substitution eliminates the need for iterative approximation processes, achieving both high precision spatial resolution and fast processing speeds by using closed-form solutions rather than numerical approximations.
Solution Approach 2:
The patent changes the mathematical parameters used in wavenumber matching from approximate interpolation coefficients to exact Fourier transform pairs. By using the Fourier transform to compute wavenumber spectra and then applying precise inverse transforms with complex exponential functions, the system achieves exact wavenumber matching without approximation errors, thereby improving spatial resolution while maintaining processing efficiency.
2Loss of time
If approximate interpolation processings are performed for beamforming, then calculation time is reduced, but productivity and processing speed decrease
Solution Approach 1:
The patent performs preliminary Fourier transform computations to obtain wavenumber spectra before the actual beamforming process. By pre-computing the spectral representations and preparing the complex exponential functions in advance, the system eliminates the need for time-consuming approximate interpolations during real-time beamforming, thereby significantly improving processing speed without sacrificing accuracy.
Solution Approach 2:
The patent substitutes approximate numerical interpolation algorithms with exact analytical solutions using Fourier transforms and complex exponential functions. This replacement eliminates iterative approximation processes and enables direct computation of beamformed signals, achieving both reduced processing time and maintained high productivity in real-time applications.
3Measurement precision
If high accuracy wavenumber matching is implemented without approximate interpolations, then measurement precision improves, but device complexity increases
Solution Approach 1:
The patent implements a universal beamforming algorithm that handles arbitrary aperture geometries and multidimensional arrays using a single unified approach based on Fourier transforms and wavenumber matching. This multi-functional method simultaneously achieves high spatial resolution accuracy and manages computational complexity by using standard mathematical operations that can be efficiently implemented across different array configurations without requiring separate specialized algorithms for each case.
Data Source
AI summary
Beamforming method that allows a high speed and high accuracy beamforming with no approximate interpolations. This beamforming method includes step (a) that generates reception signals by receiving waves arrival from a measurement object; and step (b) that performs a beamforming with respect to the reception signals generated by step (a); and step (b) including without performing wavenumber matching including approximate interpolation processings with respect to the reception signals, and the reception signals are Fourier's transformed in the axial direction and the calculated Fourier's transform is multiplied to a complex exponential function expressed using a wavenumber of the wave and a carrier frequency to perform wavenumber matching in the lateral direction and further, the product is Fourier's transformed in the lateral direction and the calculated result is multiplied to a complex exponential function, from which an effect of the lateral wavenumber matching is removed, to perform wavenumber matching in the axial direction, by which an image signal is generated.