A Design Method of Various Filters Utilizing an Adaptive Filter with Restricted Algebraic Moment of Weight

In this paper we propose a design method of the various filters utilizing an adaptive filter that has the restricted algebraic moment of the weight. When an amplitude sampling filter such as the surface acoustic wave filter or a digital filter are realized, the dispersion of the weight of these filters becomes a problem. This dispersion is given by the algebraic moment of degree N of the weight in this paper. The adaptive system consists of the ideal filter and an adaptive filter that estimates the impulse response of the ideal filter. The adaptive algorithm is a gradient algorithm by which the algebraic moment of the weight was restricted. We prove the existence of the unique convergence value of the weight and formulate the convergence condition of the adaptive algorithm. As a result, the design of the filter that has the restricted algebraic moment of the weight becomes easy, and the application of this design technology extends widely. Finally, the convergence performances of this adaptive filter are verified by the computer simulation.