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Discrete-time beamforming : ウィキペディア英語版 | Discrete-time beamforming Discrete-time beamforming is a digital signal processing technique used to spatially select propagating waves (most notably acoustic and electromagnetic waves). In order to implement beamforming on digital hardware the received signals need to be discretized. This introduces quantization error, perturbing the array pattern. For this reason, the sample rate must be generally much greater than the Nyquist rate.〔(Sonar Beamforming ) users.ece.utexas.edu. Retrieved November 12, 2015〕 == Introduction == Beamforming aims to solve the problem of filtering signals coming from a certain direction as opposed to an omni-directional approach. Discrete-time beamforming is primarily of interest in the fields of seismology, acoustics, sonar and low frequency wireless communications. Antennas regularly make use of beamforming but it is mostly contained within the analog domain. Beamforming begins with an array of sensors to detect a 4-D signal (3 physical dimensions and time). A 4-D signal exist in the spatial domain at position and at time . The 4-D Fourier transform of the signal yields which exists in the wavenumber-frequency spectrum. The wavenumber represents the spatial frequency and represents the temporal frequency. The 4-D sinusoid can be rewritten as where , also known as the slowness vector.
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