LMS-optimal notch filters with improved transient performance

The use of a pole-contraction factor (α) with a value close to unity in the Constrained Notch Filters (CNFs) causes excessively long transient response. For practically useful values of α, the transient duration is reduced, on the other hand however, the error in transparency as measured by the MSE is increased. In this paper, we increase the order of CNFs by a strategic pole/zero placement to address this tradeoff. Two approaches of finding these pole/zero locations are shown. One of the methods is optimal in the LMS sense, while the other, though suboptimal, yields a closed-form solution. The resulting filters show a significant improvement in the transient duration