A planar active sound control system using two-dimensional spatial harmonics

An active sound control system based on the extraction of orthogonal spatial harmonics is considered. The system comprises two parallel planar rectangular receiving arrays consisting of small monopole receivers and two planar rectangular transmitting arrays (installed parallel to the receiving arrays) consisting of small monopole transmitters. The field received by the receiving arrays is approximated by a finite number of propagating plane waves with the help of the Fourier transform. The transmitting arrays excite the same set of plane waves outside the system, their amplitudes being chosen so as to cancel the incident external field in a certain region near the system behind the transmitting arrays. The performance of the system is considered for both continuous and discrete distributions of transmitters and receivers. Allowance is made for random errors in the transmitters and receivers, individual to each device.