Transducer sensitivity compensation using diagonal preconditioning for time reversal and Tikhonov inverse filtering in acoustic systems

Abstract

Filters are commonly used in sound reproduction and communication systems as a means of compensating for the response of the electro-acoustic plant. Two commonly used filter designs in the field of acoustics are the time reversal filter and the Tikhonov inverse filter. In this paper the influence of transducer sensitivities on the performance of these filters is examined. It is shown that the sensitivity of the transducers can negatively affect the performance of the resulting filter. To compensate for the decrease in performance, diagonal preconditioning can be implemented in the system. It is shown that by using diagonal matrices, which minimize the condition number of the system, the loss in performance arising from unbalanced sensitivities is minimized. This paper proposes an algorithm to find such a set of diagonal matrices and results are presented showing the improvements in performance arising from the modified filter design.