In this paper, we propose an online adaptation method for Fourier series-based acoustic transfer function (FS-ATF) models for robot audition systems using microphone array signal processing. The ATF represents the characteristics of signal propagation from a sound source to a microphone, which is essential for sound source localization (SSL) and sound source separation (SSS). For practical applications in dynamically changing real-world environments, ATF models must satisfy two criteria: (1) they must be adaptable to changes in the acoustic environment; and (2) they must be lightweight to be suitable for resource-constrained systems, such as robots with limited memory and computational capacity. The proposed method addresses these challenges using Fourier series expansions for interpolation, which reduces the memory footprint of the ATF model and facilitates online adaptation to acoustic environmental changes. The experimental results demonstrate that the proposed online adaptation method both improves the SSL and SSS performance while reducing the size of the ATF model, which represents a significant improvement over existing online ATF adaptation methods.