This paper presents a recursive solution to the Broadband Acoustic Contrast Control with Pressure Matching (BACC-PM) algorithm, designed to optimize sound zones systems efficiently in the time domain. Traditional frequency-domain algorithms, while computationally less demanding, often result in non-causal filters with increased pre-ringing, making time-domain approaches preferable for certain applications. However, time-domain solutions typically suffer from high computational costs as a result of the inversion of large convolution matrices. To address these challenges, this study introduces a method based on gradient descent and conjugate gradient descent techniques. By exploiting recursive calculations, the proposed approach significantly reduces computational time compared to direct inversion. Theoretical foundations, simulation setups, and performance metrics are detailed, showcasing the efficiency of the algorithm in achieving high acoustic contrast and low reproduction errors with reduced computational effort. Simulations in a controlled environment demonstrate the advantages of the method.
