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A proof of the Woodward‐Lawson sampling method for a finite linear array
Author(s) -
Somers Gary A.
Publication year - 1993
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/93rs00591
Subject(s) - equidistant , mathematics , aperture (computer memory) , sampling (signal processing) , lattice (music) , finite set , wavelength , mathematical analysis , geometry , optics , physics , detector , acoustics
An extension of the continuous aperture Woodward‐Lawson sampling theorem has been developed for a finite linear array of equidistant identical elements with arbitrary excitations. It is shown that by sampling the array factor at a finite number of specified points in the far field, the exact array factor over all space can be efficiently reconstructed in closed form. The specified sample points lie in real space and hence are measurable provided that the interelement spacing is greater than approximately one half of a wavelength. This paper provides insight as to why the length parameter used in the sampling formulas for discrete arrays is larger than the physical span of the lattice points in contrast with the continuous aperture case where the length parameter is precisely the physical aperture length.