Standard linear array: Difference between revisions

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A standard linear array (SLA) is a linear array of interconnected transducer elements, e.g. microphonemicrophones or antennaantennas, elements where the individual elements are uniformly weighted (un-tapered) and arranged in a straight line spaced at one half of the smallest wavelength of the intended signal to be received and/or transmitted.<ref>{{cite book |last1=Van Trees |first1=H.L. |title=Optimum Array Processing |page=51}}</ref> The reason for this spacing is that it prevents [[grating lobes]] in the [[visible region]] of the array.<ref>{{cite book |last1=Richards |first1=M.A. |title=Principles of Modern Radar: Basic Principles |publisher=Scitech Publishing |___location=Edison, NJ |pages=330-332}}</ref>

Intuitively one can think of a linear array of elements as spatial sampling of a signal in the same sense as time sampling of a signal. Per Shannon's [[sampling theorem]], the sampling rate must be at least twice the highest frequency of the desired signal in order to preclude spectral aliasing. The [[discrete-time Fourier transform]] (DTFT) of a sampled signal is always periodic, producing "copies" of the spectrum at intervals of the sampling frequency. The analog of radian frequency in the time ___domain is [[wavenumber]], <math>k = \frac{2\pi}{\lambda}</math> radians per meter, in the spatial ___domain. Therefore the spatial sampling rate, in samples per meter, must be <math>\geq 2 \frac{samples}{cycle} \times \frac{k \frac{radians}{meter}}{2\pi \frac{radians}{cycle}}</math>. ThereforeThe sampling interval, which is the inverse of the sampling intervalrate, in meters per sample, must be <math>\leq \frac{\lambda}{2}</math>.

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