Short pulse scattering signals furnish valuable information for classification or identification. The aim in this paper is toward defining a strategy for parameterization of the field in terms of “physical observables” which are distinct features that show up in the radar signature at early or late time windows. For targets comprising of open-ended enclosures with interior-exterior coupling, distinct late time observables may be found in the form of high-Q resonances. An effective parameterization is therefore provided by a hybrid representation wherein the internal fields are expressed as resonances while the wave interactions around the exterior boundaries, which are important essentially at early times, are expressed in terms of rapidly decaying series of rays (or wavefronts). This hybrid concept is illustrated here for the prototype configuration of an open-ended perfectly conducting parallel plate waveguide cavity. The hybrid formulation utilizes a systematic matrix procedure in which all the scattering coefficients are expressed in a generic form so that it may be generalized to other open cavity configurations; the specific coefficients for the present configuration are summarized in an appendix. The properties of the hybrid parameterization are contrasted with those of the global SEM representation. Numerical calculations of the time-dependent field and approximate models for the late time observables are considered in Parts II and III of this sequence.