Normal mode representations are useful in many aspects of underwater acoustics, e.g., modal acoustic tomography uses precise measurements of the travel time of broadband pulses to invert for environmental parameters. A thorough understanding of the resolution of mode estimators is crucial for tomographic applications. Typically, acoustic modes are used for describing and analyzing the temporal and spatial structure of narrow-band signals. As source bandwidth increases, however, mode estimation algorithms can no longer ignore frequency variations of the modal wave numbers, which result in temporal dispersion and frequency-dependent mode shapes. To address the issue, this study establishes an array processing framework for estimating the modal composition of broadband receptions. Within this framework, the time/frequency resolution tradeoffs inherent in the processing of modal pulse arrivals are explored. Specifically, the effects of mode shape frequency variations on standard modal beamformers are investigated. In addition to characterizing the performance of spatial filters for mode separation, this study considers the problem of designing receivers to compensate for the dispersion (pulse-spreading) introduced by the waveguide. Techniques developed through theoretical work have been applied to data from the Acoustic Thermometry of Ocean Climate (ATOC) project. Some results of modal time series analysis for 1996 ATOC receptions are presented.