New methods for the design of recursive digital filters in the time domain

This paper presents new methods for the design of optimal and suboptimal recursive digital filters in the time domain. The proposed methods are based on the approximation of the desired impulse response of a digital filter. Since the duration of impulse response of a recursive digital filter is not finite, it is desirable to use an infinite interval performance index from the point of stability. First, a method for the design of an optimal recursive digital filter is presented. The optimal solution is obtained by minimizing the given infinite interval performance index. Multivariable optimization techniques such as the Fletcher-Powell method can be applied to obtain the optimal solution. However, when the order of a filter becomes high, it is difficult to obtain the optimal solution. Next, suboptimal recursive digital filters with parallel and cascade structures are proposed. When these methods are used, it becomes easy to design a high-order suboptimal filter. Various numerical examples are shown to illustrate the results in detail.