Unified Method of Calculating Impulse Response and Frequency Response in Piezoelectric Transducer with Inhomogeneous Structure

Both of impulse response and frequency response in a piezoelectric transducer with some inhomogeneous structure can be calculated in a unified and systematic manner using the concept of "probabilistic superposition" of energy modes in a multi-layered system that is wavelet-analyzed. The input-output, propagation, reflection and transmission of energy modes in the multi-layered transducer can be expressed with some appropriate matrix operation on energy modes, and the probabilistic superposition of such energy modes provides either the impulse response or the frequency response, according to how the superposition is performed, based on the uncertainty principle between time and frequency. In addition, the wavelet analysis of the spatial inhomogeneous structure of the transducer enables us to treat the problem in a step-by-step manner from lower resolution level to higher one.