A new approach to the design of discrete coefficient FIR digital filters

In this correspondence, the iterative Lagrange multiplier approach is proposed for designing discrete coefficient FIR digital filters. The method associates the conventional Lagrange multiplier approach and a tree search algorithm. For each branch of the tree, the Lagrange multiplier approach is used to optimize the remaining unquantized coefficients of the designed FIR filter in the least-squares sense when one or more of the coefficients takes on discrete values. Design examples, including general low-pass filters and Nyquist filters, are presented to demonstrate the effectiveness of the method. Also, the method can be extended to design discrete coefficient 2-D FIR filters