Standard linear array

A standard linear array (SLA) is a linear array of interconnected transducer, e.g. microphone or antenna, elements where the individual elements are arranged in a straight line spaced at one half of the wavelength of the intended signal to be received and/or transmitted. The reason for this spacing is that it prevents grating lobes in the visible region of the array. 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. The analog of radian frequency in the time domain is wavenumber in the spatial domain. Wavenumber, $k={\frac {2\pi }{\lambda }}$ radians per meter. Therefore the spatial sampling rate, in samples per meter, must be $\geq 2\times {\frac {k}{2\pi }}$. Therefore the sampling interval, in meters per sample, must be $\leq {\frac {\lambda }{2}}$.