Optimal least-squares design of pipelined recursive filters in the time-domain

Look-ahead pipelined recursive filters are primarily obtained from a given transfer function. However, Chien-Piao Lan and Chien Wei Jen (1994) designed the pipelined filters directly from the time-domain specifications using the modified least-squares approximation. In this paper, we present an algorithm for optimal least-squares estimation of the coefficients of recursive filters in look-ahead pipelined form. The method minimizes the norm of the true fitting error between the prescribed and the estimated impulse responses by first theoretically decoupling the numerator and denominator estimation into two separate subproblems. A simple algorithm is then presented for iterative estimation of the denominator, whereupon the numerator can be obtained in a single step. Some examples and comparison with an existing method are provided to illustrate the proposed algorithm.