Design of finite-wordlength IIR digital filters in the time/spatial domain

An effective method is proposed to design discrete coefficient IIR digital filters in the time/spatial domain in this paper. The method associates the 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 IIR filters when one or more of the coefficients takes on discrete values, such that the actual filter gives the best approximation to the ideal impulse response. For each node of the tree, one more unquantized coefficient is chosen to take on discrete values until all coefficients are quantized. The method is simple and effective, and the stability of the designed filters is easily obtained if the length of the dealed impulse response is long enough. Moreover, the method can be used to design 2-D discrete coefficient IIR digital filters as well as 1-D IIR digital filters.