This paper demonstrates how flexural wave propagation in a thin plate can be modeled by estimating the combined effect of the excitation source signal and the impulse response of the ultrasonic sensor. The wave propagation in the plate is modeled using the wave equation for the flexural wave mode. A theoretical model for flexural wave propagation in thin plates has been derived, and it has been compared with measurements excited by tapping gently on the surface. The combined effects of the excitation source signal and the impulse response of the low-cost piezoelectric sensor are modeled using finite-impulse response and/or infinite-impulse response filters. Thereafter, the performances of the selected filters are compared on estimating the wave propagation in a thin quartz glass plate. Results indicate that the most accurate estimation of wave propagation has been obtained using a linear phase filter which attributes all dispersions to the flexural wave.