A projected least-squares approach to constrained Nyquist filter design

Least-squares design of Nyquist filter with specified passband and stopband ripples relates to a constrained FIR filter design problem with constraints in time- and frequency-domain. This paper deals with these constraints uniformly, and formulates the design problem as a quadratic programming problem with equality and inequality constraints. A novel and efficient algorithm is presented; it is referred to as a projected least-squares algorithm. The algorithm first computes the unconstrained minimization solution of the quadratic cost function, and then projects it successively onto the boundaries of the active constraints of the problem. The algorithm is much more efficient than the existing active-set method for quadratic programming problems. Design examples demonstrate the high efficiency of the algorithm.