Study of signal treatment for a pulsed electro-acoustic measurement cell: a way of improving the transfer matrix condition number

This work is focused on the improvement of the condition number of the transfer function matrix in a pulsed electro-acoustic (PEA) cell. A numerical electro-acoustic model is developed with the software COMSOL. This model is one-dimensional and the system of equations with partial differential functions is solved using a finite element method in non-stationary situations. Using this model, we can establish the output voltage of the piezoelectric sensor and acoustic pressure at each point of the calculation domain. Our approach consists in recovering the charge distribution within the sample using a deconvolution method between the simulated output voltage and the transfer function of the PEA cell. Results show why some changes of the PEA cell such as the nature of materials or sensor geometry involve an ill-posed problem or ill-conditioned problem, and why other arrangements lead to a well-conditioned problem, more amenable to giving the appropriate solution.