Fast Time-Varying Exponentiated Convolution Methods for Generative Direction Dependent Reverberation

Spherical harmonic encoded acoustic sound-fields capture directional characteristics of room impulse responses that are useful for accurate spatial audio reproduction. However, high costs of multi-microphone measurements and numerical simulations motivate alternative data-set augmentation and synthetic data generation methods that supplement small collections. This paper introduces time-varying exponentiated convolution methods that transform both Gaussian noise and impulse responses into reverberation and modified spectral-decay fields respectively. We derive two recursive and fast convolution algorithms that extend into the spherical harmonic domain, model smooth reverberation time distributions with non-stationary Gaussian processes, and realize an optimal filter design. Experiments evaluate computational performance, and validate out-of-distribution generated impulse responses.