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On the Necessary Delay for the Design of Causal and Stable Recursive Inverse Filters for Loudspeaker Equalization

The authors have developed and applied a novel approach to the equalization of non-minimum phase loudspeaker systems, based on the design of Infinite Impulse Response (recursive) inverse filters. In this paper the results and improvements attained on this novel IIR filter design method are presented. A special attention has been given to the delay of the equalized system. The boundaries to be posed on the search space of the delay for a causal and stable inverse filter, to be used in the nonlinear least squares minimization routine, are studied, identified and related with the phase response of a test system (to be equalized) and with the order of the inverse filter; finally, these observations and relations are extended and applied to multi-way loudspeaker systems, demonstrating the connection of the lower and upper bounds of the delay with the loudspeaker’s crossover filters phase response and inverse filter order.

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