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Active noise control (ANC) over an extended spatial region using multiple microphones and multiple loudspeakers has become an important problem. The maximum noise reduction (NR) potential over the control area is a critical evaluation variable as it indicates the fundamental limitation of a given ANC system. In this paper, a method to mathematically formulate the NR potential for any given multichannel ANC systems is developed. First, the residual error in the multichannel feedforward ANC system is formulated, and then the multiple-input-multiple-output problem is decomposed into the parallel-channel problem. The total energy of the residual error is further decomposed into three different terms representing (i) the signal coherence between the reference signals and error signals, (ii) the filter, and (iii) the system null space. The experimental results validate the proposed evaluation method and illustrate the effectiveness on the maximum NR performance evaluation for given systems. Using the proposed analyzing method, more insight into the contribution of each component to the NR potential can be achieved.

Dynamic binaural rendering of Ambisonics considering head movements gives a highly realistic sensation to listeners owing to the precise localization and the presence of dynamic cues. Dealing with a head movement is often achieved in the spherical harmonic domain by multiplying Ambisonic signals by a Wigner D-matrix (WDM) with the aim of rotating signals in the opposite direction to the head movement. However, for a vertical rotation, the system requires an enormous computational cost owing to the structure of the WDM, whose number of block diagonal elements increases with the spherical harmonic order of Ambisonics. In this paper, a method is introduced to reduce the computational cost related to the vertical rotation by approximating a WDM with a banded WDM generated from the truncated sum of a power series expression of the WDM. By using an analytically derived upper bound of the approximation error, two methods are devised to determine the minimum bandwidth which archives the maximum computational cost reduction under the user-preferred threshold. The experimental results show that there is a trade-off between the approximation error and the computational cost and that these methods are applicable to the use case of interest, i.e., dynamic binaural rendering of Ambisonics.