Differentiable Active Acoustics: Optimizing Stability via Gradient Descent

Active acoustics (AA) refers to an electroacoustic system that actively modifies the acoustics of a room. For common use cases, the number of transducers---loudspeakers and microphones---involved in the system is large, resulting in a large number of system parameters. To optimally blend the response of the system into the natural acoustics of the room, the parameters require careful tuning, which is a time-consuming process performed by an expert. In this paper, we present a differentiable AA framework, which allows multi-objective optimization without impairing architecture flexibility. The system is implemented in PyTorch to be easily translated into a machine-learning pipeline, thus automating the tuning process. The objective of the pipeline is to optimize the digital signal processor (DSP) component to evenly distribute the energy in the feedback loop across frequencies. We investigate the effectiveness of DSPs composed of finite impulse response filters, which are unconstrained during the optimization. We study the effect of multiple filter orders, number of transducers, and loss functions on the performance. Different loss functions behave similarly for systems with few transducers and low-order filters. Increasing the number of transducers and the order of the filters improves results and accentuates the difference in the performance of the loss functions.