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	ソナー方程式	Beamforming
分野	音響学	音響学
系統	Process / pipeline	Process / pipeline
提唱年	1983	1988
提唱者	Robert Urick	Van Veen, Barry Buckley
種類	Underwater acoustic detection framework	Directional audio array processing
原典	Urick, R. J. (1983). Principles of Underwater Sound (3rd ed.). McGraw-Hill. ISBN: 978-0070660816	Van Veen, B. D., & Buckley, K. M. (1988). Beamforming: A versatile approach to spatial filtering. IEEE ASSP Magazine, 5(2), 4–24.
別名	active sonar equation, passive sonar equation, underwater detection, acoustic range equation	beamformer, spatial filtering, microphone array, phased array
関連	5	5
概要	The sonar equation is a fundamental framework for predicting the detection range and performance of active and passive sonar systems in underwater environments. Systematized by Robert Urick in his seminal 1983 work, the sonar equation quantifies the acoustic signal-to-noise ratio (SNR) needed for detection, accounting for source level, propagation loss, noise characteristics, and receiver sensitivity. It is the cornerstone of underwater acoustic system design, naval detection systems, marine research, and subsea communication.	Beamforming is a spatial signal processing technique that uses microphone arrays to selectively enhance sound from a desired direction while suppressing sounds from other directions. Formalized by Van Veen and Buckley in 1988, beamforming is fundamental to hands-free speech communication, hearing aids, sonar, radar, and spatial audio recording. It enables 'listening' with directional sensitivity despite using omnidirectional microphones, by exploiting time delays and phase differences between array elements.