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# Designing Windows for Filtering the Ambiguity Function in Range-Doppler Radar Applications

IP.com Disclosure Number: IPCOM000037384D
Original Publication Date: 1989-Dec-01
Included in the Prior Art Database: 2005-Jan-29
Document File: 3 page(s) / 45K

IBM

## Related People

Feig, E: AUTHOR [+2]

## Abstract

A technique is described whereby two-dimensional windows are designed for use with algorithms, as used in Range-Doppler radar applications, for computing the ambiguity function around the origin.

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Designing Windows for Filtering the Ambiguity Function in Range-Doppler Radar Applications

A technique is described whereby two-dimensional windows are designed for use with algorithms, as used in Range-Doppler radar applications, for computing the ambiguity function around the origin.

Basic Range-Doppler radar relies on the computation of a portion of the ambiguity function around the origin. This computation is so costly that the function is sampled on a small set of range coordinates. Since windowed ambiguity functions are required to estimate sampled values (*), the concept described herein provides a method of generating good windows for this purpose.

The question of how to find two-dimensional windows K(x,p), whose inverse Fourier transforms have the following form is addressed. It is straightforward to see that this requires W to be of the form

First, a generalization allows windows to be viewed as images of linear operators acting on rank-one tensors. Two linear operators on L2(R) are defined L1(K)(x,y) = K(ax+by,cx+dy) where a, b, c, d e R and ad-bc * 0, and

The first operator is an invertible change of basis and the second is the Fourier transform with respect to the first variable, followed by a change of variables. Operator A is defined as the composition Observe that for functions of the form K(t,x) = f(t)g*(x) and b=c=d=1, a=0, the image of the linear operator A is precisely a window of the type desired. Therefore, the tensor-product notation (fRg*)(x,y) = f(x)g* (y) is used. In the following, the inner products will be evaluated of the form < A(fRg*), K > + < fRg*, A*(K) > where, as usual, A* denotes the adjoint of A.

Every K e L2(R) acts on L2(R2) as a Hilbert-Schmidt...