Mathematical analysis and interpretation of pulsed electro-acoustic system

A mathematical analysis, which results in an improved understanding of the pulsed electro-acoustic (PEA) system and a correct interpretation of the PEA signals, is made of the fundamental measurement principle by introducing the theory of signals and systems. As a result, the overall measurement system, without consideration of the attenuation and dispersion effects in the acoustic wave propagation, can be equivalently turned into and modeled by a linear time-invariant (LTI) system with a charge-wave function as its input. From this model, it is revealed that the measured PEA signal is not linearly proportional to, but is interpreted as a weighted running-average of, the real space charge distribution. The impulse response of the LTI system, acting as the weighting function, can be employed for the assessment of the system quality and should be given together with the measured PEA signals for evaluating the space charge distribution.