Driven by the need for describing and understanding wave propagation in structural materials and components, several analytical, numerical, and experimental techniques have been developed to obtain dispersion curves. Accurate characterization of the structure (waveguide) under test is needed for analytical and numerical approaches. Experimental approaches, on the other hand, rely on analyzing waveforms as they propagate along the structure. Material inhomogeneity, reflections from boundaries, and the physical dimensions of the structure under test limit the frequency range over which dispersion curves can be measured. In this work, a new data-driven modeling approach for estimating dispersion curves is developed. This approach utilizes the relatively easy-to-measure, steady-state Frequency Response Functions (FRFs) to develop a state-space dynamical model of the structure under test. The developed model is then used to study the transient response of the structure and estimate its dispersion curves. This paper lays down the foundation of this approach and demonstrates its capabilities on a one-dimensional homogeneous beam using numerically calculated FRFs. Both in-plane and out-of-plane FRFs corresponding, respectively, to longitudinal (the first symmetric) and flexural (the first anti-symmetric) wave modes are analyzed. The effects of boundary conditions on the performance of this approach are also addressed.