The Research Of Least Squares Techeniques For Stable IIR Digital Filter

This paper considers the design of the IIR (infinite impulse response) digital filter, mainly the iterative weighted least squares design methods. In order to satisfy the amplitude response of the filter, we add constraints of amplitude on different frequency bands, and analyze the influence of the maximal amplitude error on the design results. To obtain better design results with equiripple error, we apply iterative reweighted techniques to the design of IIR digital filters. Since a success of quadratic programming need to be solved in the weighted least squares algorithm, the project least squares algorithm substitutes for the popular active set methods so as to gain a faster speed. The paper is arranged in five sections.The first section mainly introduces the advantages of IIR digital filters and the resent research of IIR digital filters. It also presents two improvements of iterative least squares algorithm, that is, adding amplitude constraints and introducing iterative reweighted techniques. Some design examples are presented to illustrate the performance. Some different stable constraints are analyzed, and their importance to IIR digital filter is shown. Lastly, it introduces project least squares algorithm.The second section introduces some fundamental conceptions and two design criterions of IIR digital filter. It formulates the design problem based on weighted least squares design criterion, and emphasizes the stable constraints that IIR filter design must guarantee.