Design of Nonrecursive Filters Satisfying Arbitrary Magnitude and Phase Specifications Using a Least-Squares Approach

A method is described which can be used to design nonrecursive filters satisfying prescribed magnitude and phase specifications. The method is based on formulating the absolute mean-square error between the frequency response of the practical filter and the desired response as a quadratic function. The coefficients of the filters are obtained by solving a set of linear equations. It is shown that our method, in general, has an order of magnitude lower computational complexity than the eigenfilter method. For the design of allpass filters, in particular, the computational complexity is three orders of magnitude lower than the eigenfilter method. In addition, our method yields a lower mean-square error.