Most acoustic sources found in the ocean environment are spatially complex and broadband. In the case of shallow water propagation, these source characteristics complicate the analysis of received acoustic data considerably. A common approach to the broadband problem is to decompose the received signal into a set of narrow-band lines. This then allows the problem to be treated as a multiplicity of narrow-band problems. Here a model-based approach is developed for the processing of data received on a vertical array from a broadband source where it is assumed that the propagation is governed by the normal-mode model. The goal of the processor is to provide an enhanced (filtered) version of the pressure at the array and the modal functions. Thus a pre-processor is actually developed, since one could think of several applications for these enhanced quantities such as localization, modal estimation, etc. It is well-known that in normal-mode theory a different modal structure evolves for each temporal frequency; thus it is not surprising that the model-based solution to this problem results in a scheme that requires a “bank” of narrow-band model-based processors—each with its own underlying modal structure for the narrow frequency band it operates over. The “optimal” Bayesian solution to the broadband pressure field enhancement and modal function extraction problem is developed. It is shown how this broadband processor can be implemented (using a suboptimal scheme) in pseudo real time due to its inherent parallel structure. A set of noisy broadband data is synthesized to demonstrate how to construct the processor and achieve a minimum variance (optimal Bayesian) design. It is shown that both broadband pressure-field and modal function estimates can be extracted illustrating the feasibility of this approach.