A new strategy to reduce the truncation error in near-field/far-field transformations

A new strategy to reduce the far-field reconstruction error due to the finite size of the measurement region in planar and cylindrical near-field/far-field transformation techniques is presented. The approach exploits the (spatial) band-limitation property of the radiated field in order to estimate the field outside the measurement area. A number of different estimation algorithms are investigated, with reference to both the accuracy of the estimation and the required computational effort. Numerical and experimental results show that with a small computational effort, it is possible to obtain a significant improvement of the reconstructed far-field pattern with respect to that obtained without near-field extrapolation.

[1]  Paulo Jorge S. G. Ferreira,et al.  Incomplete sampling series and the recovery of missing samples from oversampled band-limited signals , 1992, IEEE Trans. Signal Process..

[2]  G. Franceschetti,et al.  On the degrees of freedom of scattered fields , 1989 .

[3]  Mario Bertero,et al.  Linear inverse problems with discrete data. I. General formulation and singular system analysis , 1985 .

[4]  R. Wittmann,et al.  The receiving antenna as a linear differential operator: Application to spherical near-field scanning , 1985 .

[5]  O. Bucci,et al.  Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples , 1998 .

[6]  C. Micchelli,et al.  Optimal Estimation of Linear Operators in Hilbert Spaces from Inaccurate Data , 1979 .

[7]  B. Roy Frieden,et al.  VIII Evaluation, Design and Extrapolation Methods for Optical Signals, Based on Use of the Prolate Functions , 1971 .

[8]  Paulo Jorge S. G. Ferreira,et al.  Noniterative and fast iterative methods for interpolation and extrapolation , 1994, IEEE Trans. Signal Process..

[9]  Paulo Jorge S. G. Ferreira.  The stability of a procedure for the recovery of lost samples in band-limited signals , 1994, Signal Process..

[10]  Yahya Rahmat-Samii,et al.  The bi-polar planar near-field measurement technique, part I: implementation and measurement comparisons , 1994 .

[11]  D. Slepian,et al.  Prolate spheroidal wave functions, fourier analysis and uncertainty — II , 1961 .

[12]  Bede Liu,et al.  On the use of singular value decomposition and decimation in discrete-time band-limited signal extrapolation , 1984 .

[13]  J. Cadzow,et al.  An extrapolation procedure for band-limited signals , 1979 .

[14]  A. C. Newell,et al.  Error analysis techniques for planar near-field measurements , 1988 .

[15]  M. Bertero,et al.  Linear inverse problems with discrete data: II. Stability and regularisation , 1988 .

[16]  A. Sano,et al.  Optimally regularized inverse of singular value decomposition and application to signal extrapolation , 1993, Signal Process..

[17]  M. Bertero.  Linear Inverse and III-Posed Problems , 1989 .

[18]  A. Papoulis.  A new algorithm in spectral analysis and band-limited extrapolation. , 1975 .

[19]  Ii R. Marks.  Restoring lost samples from an oversampled band-limited signal , 1983 .

[20]  G. Franceschetti,et al.  On the spatial bandwidth of scattered fields , 1987 .