The theory of multiresolution decomposition and wavelets is used to study the effective properties of a thin elastic plate with surface mass density or stiffness heterogeneity, subjected to time-harmonic forcing. The heterogeneity possesses micro- and macro-scale variations, and has a macroscale outer dimension. It is shown that the microscale mass variation has practically no effect on the macroscale plate response, whereas microscale stiffness variation can have a significant effect. We derive an effective constitutive relation pertaining to a microscale stiffness variation. It is shown that it is possible to synthesize classes of different stiffness microstructures that have the same footprint on the macroscale component of the plate response. An effective, smooth, stiffness heterogeneity associated with the classes is developed. The results are first derived analytically and then supported by numerical simulations.