Deep Preprocessing Method for Speech Restoration in Parametric Array Loudspeakers via Time-Frequency Domain Modeling

The parametric array loudspeaker inherently introduces baseband distortions in directional sound applications due to the nonlinear process in air. Recently, DNNs have been used to model this forward process and to generate preprocessed signals for distortion-free speech restoration. However, when trained on real-world audio, the preprocessing network can exploit weaknesses in the forward model, producing adversarial outputs. To address it, we propose a reorganization strategy for the two-stage framework, comprising a causal TF-GridNet for preprocessed signal generation and a modified time-frequency (T-F) domain differential Volterra Filter (DiffVF) as the forward model. The causal TF-GridNet estimates real and imaginary components using a T-F band-split mechanism. The modified forward model integrates the second-order difference and kernel convolution operations of the original time-domain version into the T-F domain, preserving interpretability while stabilizing training. A refined $N$th-order equalization, based on the T-F domain DiffVF model, is implemented as a competitive baseline. Simulated and real-world experiments demonstrate state-of-the-art reconstruction performance of the proposed method across various objective metrics.