A successive projections method with a changeable maximum allowable deviation

A applicability of Successive Projections (SP) method is wide. In the previous SP method which is an iterative approximation method, only one extreme frequency point at which the deviation from the given specification is maximized is used in the update of the filter coefficients. We extended to SP method which can update the filter coefficients by the multiple extreme frequency points using Fritz John´s theorem. In this method, the solution is obtained less iteration number than the previous method. However, because it is necessary to decide the maximum allowable error experientially, there is the case that the solution does not converge and the obtained filter does not have equiripple characteristics. In this paper, we present a design method of linear phase FIR filters by SP method updating maximum allowable error. The updating maximum allowable error analytically solves such as Remez algorithm. Finally, we confirm the effectiveness of propose method through several examples.