On bandwidth of broadband wavefields observed over spatial regions

This paper presents a characteristic expression to determine the effective bandwidth of broadband wavefields observed over a source-free finite spherical region. To address this topic, for given constraints on size of the observation region and bandwidth, we characterize the observable wavefield using modal expansion of wave propagation in 3D. When signals are transmitted to a spatially constrained region, an infinite number of spatial modes are excited in the spatial region. Our analysis shows that though the effective bandwidth at the lower spatial modes is equal to the given frequency bandwidth, the effective bandwidth drops as mode index increases depending on the acceptable signal to noise ratio (SNR) at each spatial mode. Further, beyond a certain spatial mode, the effective bandwidth becomes zero. Thus, we can truncate the infinite representation to a finite number of spatial modes. In addition, the effective spatial modes represent the number of independent channels. In the context of broadband communications, these findings indicate that only a finite number of independent channels are available to carry information, each with an effective bandwidth.