A linearly constrained minimization approach to adaptive linear phase and notch filters

The linearly constrained least-squares problems are implemented using unconstrained formulation and applied to both adaptive prediction and estimation. This formulation is similar to the one used in the generalized sidelobe canceler, where the constraints are incorporated through a decomposition of the weight vector into constraint-dependent components and other components which are determined by the application and can be found from the data using adaptive techniques. The authors formulate the nonadaptive components of the constraint weight vector for linear phase filters and notch filters, which are commonly used in various applications in signal processing. The mechanism used to enforce even symmetry of the filter weights as well as a pair of complex-conjugate zeros of the filter polynomial in the unconstrained minimization is detailed.<>