Back to results
US 5,471,435 AGranted
Method for acoustic/electromagnetic signal processing
AssigneeMarshall Acoustics Pty., Ltd.
InventorRichard A. Marschall
Life of this patent
Estimating the term…
Abstract
A process for predictively modelling potential fields in inhomogeneous media is particularly suited for implementation as a Digital Signal Processing chip, as it rapidly predicts the potential field by repeatedly perturbing a trial field solution by a step approximation to the known inhomogeneous media, and then, with one Fast Fourier Transform and one Inverse Fast Fourier Transform, creates a second estimated field solution; a fixed number of such iterations provides a final potential field model, which may be compared with a sensed field to predictively adapt sensor arrays or beam shaping.
Claims18
A process for modelling an acoustic or electromagnetic field at a given wave number in an inhomogeneous medium comprising:
- setting a grid of locations within the medium, x,
- determining a medium model set of data points corresponding to the wave field, G.sub.0 (x), and the wave velocity in a homogeneous medium at each said location;
- forming sequentially a fixed number of perturbed data sets .alpha..sub.1 (x)G.sub.0 (x), . . . ,.alpha..sub.n (x)G.sub.n-1 (x), each intermediate a set of data points corresponding to the homogeneous medium and the n-th medium model of data points, for each said perturbed data set, the data corresponding to a location sequentially changing from the data for a homogeneous medium to the data in the n-th medium model;
- said perturbed data sets being the product of a step-wise increasing perturbation function, .alpha.(x), and the initial homogeneous medium model and iteratively successively produced approximate models;
- forming the Fast Fourier Transform {.alpha..sub.m (x)G.sub.m-1 (x)} of said product;
- forming the transformed product ##EQU11## where k.sub.0.sup.2 is the constant part of the wave number squared and .OMEGA. is the transformed space coordinates;
- forming the Inverse Fast Fourier Transform of the transformed product to produce a new approximate model;
- repeating the procedure n times;
- and:
- outputting the resulting n-th model against the chosen location grid, x, as the wave field model of the acoustic or electromagnetic field.
7 more elements
A process for modelling;
- an acoustic or electromagnetic field at a given wave number in an inhomogeneous two-dimensional (x,z) medium comprising the steps of:
- forming as an input parameter an approximation to the field solution G.sub.m-1 (x,z), said initial approximation being in the form of a set of data points corresponding;
- to the wave field at a grid of locations for a homogeneous medium,
- perturbing the set of data points with the wave number perturbation function .alpha..sub.m (x,z) by forming the product .alpha..sub.m (x,z)G.sub.m-1 (x,z) where .alpha..sub.m (x,z) is a sequence such that .alpha..sub.0 (x,z)=0 and .alpha..sub.n =.alpha.(x,z),
- forming the Fast Fourier Transform of the product:
- {.alpha..sub.m (x,z)G.sub.m-1 (x,z)}:
- forming the product ##EQU13## where k.sub.0.sup.2 is the constant part of the wave number squared and (.OMEGA..sub.x,.OMEGA..sub.z) are the transformed coordinates for (x,z),
- producing the Inverse Fast Fourier Transform of the resultant product to provide a revised approximation to the field solution, G.sub.m (x,z),
- providing the revised approximation G.sub.m (x,z) as the input parameter and repeating the procedure n times, at each repetition, step-wise increasing the perturbation function .alpha..sub.m (x,z), and
- at the end of n repetitions, outputting the resulting field against the location grid as the desired acoustic or electromagnetic field.
7 more elements
A method for producing a model of an acoustic or electromagnetic field in a three-dimensional inhomogeneous medium comprising the steps:
- expressing for said inhomogeneous medium having a spatially varying wave velocity its spatially varying wave number squared as ##EQU14## where k.sup.2 is the wavenumber squared and is a function of position (x,y,z) with a constant part of k.sub.0.sup.2 and a varying part k.sub.0.sup.2 .alpha.(x,y,z) and determining a perturbation function .alpha.(x,y,z) ##EQU15## defining a sequence of .alpha..sub.m 's such that .alpha..sub.0 =0 and .alpha..sub.n =.alpha.(x,y,z), approximating the wave field for a homogeneous medium G.sub.0 (x,y,z);
- performing the following operation iteratively n times;
- (a) form the multiplicative product of the wave number perturbations .alpha..sub.m (x,y,z) and the approximation of the wave field G.sub.m-1 (x,y,z) to produce .alpha..sub.m (x,y,z)G.sub.m-1 (x,y,z),
- (b) form the Fast Fourier Transform of the product obtained in substep (a) to produce
- {.alpha..sub.m (x,y,z)G.sub.m-1 (x,y,z)}
- (c) multiply {.alpha..sub.m (x,y,z)G.sub.m-1 (x,y,z)} by the constant component of the wave number squared k.sup.2 and subtract from -1 to produce
- -- k.sub.0.sup.2 {.alpha..sub.m (x,y,z)G.sub.m-1 (x,y,z)}
- and divide by k.sub.0.sup.2 -(.OMEGA..sub.y.sup.2 +.OMEGA..sub.x.sup.2), where (.OMEGA..sub.x, .OMEGA..sub.y, .OMEGA..sub.x) are the transformed coordinates of (x,y,z) to obtain ##EQU16## (d) form the Inverse Fast Fourier Transform of the result of substep (c) to produce a revised field approximation ##EQU17## when m=n outputting the final approximation as the model.
5 more elements
Dependencies are inferred from the claim text.