| Abstract: | The frequency response of a constrained notch filter (CNF) of Rao and Kung or Nehorai becomes ideal as the polecontraction factor α approaches unity while the transient duration approaches infinity. However, for practically useful values of α the phase and magnitude distortions so caused can reduce the allpass nature of the CNFs (i.e. the transparency property) and cause large errors. In this paper we define a measure for the transparency misadjustment and propose two suboptimal methods of minimizing these distortions. One of these methods is based on increasing the filter order by a strategic pole/zero placement. We present a closed-form solution for this method. In the second method we increase the order by manipulating the error filter associated with the standard CNF; the coefficients of the resulting filter are determined directly. an important feature of these methods is the significant improvement in the transient performance. |
