In the context of
phased array
In antenna (radio), antenna theory, a phased array usually means an electronically scanned array, a computer-controlled Antenna array, array of antennas which creates a radio beam, beam of radio waves that can be electronically steered to point ...
s, a standard linear array (SLA) is a
uniform linear array (ULA) of interconnected transducer elements, e.g. microphones or antennas, where the individual elements are arranged in a straight line spaced at one half of the smallest wavelength of the intended signal to be received and/or transmitted. Therefore, an SLA is a subset of the ULA category. The reason for this spacing is that it prevents
grating lobes
For discrete aperture antennas (such as phased arrays) in which the element spacing is greater than a half wavelength, a spatial aliasing effect allows plane waves incident to the array from visible angles other than the desired direction to be coh ...
in the visible region of the array.
Intuitively one can think of a ULA as spatial sampling of a signal in the same sense as time sampling of a signal. Grating lobes are identical to aliasing that occurs in time series analysis for an under-sampled signal.
[ Per Shannon's ]sampling theorem
Sampling may refer to:
*Sampling (signal processing), converting a continuous signal into a discrete signal
*Sample (graphics), Sampling (graphics), converting continuous colors into discrete color components
*Sampling (music), the reuse of a soun ...
, the sampling rate must be at least twice the highest frequency of the desired signal in order to preclude spectral aliasing. Because the beam pattern (or array factor) of a linear array is the Fourier transform of the element pattern, the sampling theorem directly applies, but in the spatial instead of spectral domain. The discrete-time Fourier transform
In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of discrete values.
The DTFT is often used to analyze samples of a continuous function. The term ''discrete-time'' refers ...
(DTFT) of a sampled signal is always periodic, producing "copies" of the spectrum at intervals of the sampling frequency. In the spatial domain, these copies are the grating lobes. The analog of radian frequency in the time domain is wavenumber
In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of ...
, radians per meter, in the spatial domain. Therefore, the spatial sampling rate, in samples per meter, must be . The sampling interval, which is the inverse of the sampling rate, in meters per sample, must be .
References
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Antennas (radio)
Phased arrays