Nonrecursive digital filters: Design methods for achieving specifications on frequency response

A simple and effective method for designing a nonrecursive digital filter is described. This method is constructed so that it is convenient to implement the resulting filter by using the fast convolution application of the fast Fourier transform. For one representative example of a fast convolution implementation of a nonrecursive digital filter designed by the method in this paper, only as many multiplications (per output sample) were required by this implementation as were required by an implementation of a well-designed recursive digital filter achieving an equally effective frequency response. This method for designing nonrecursive digital filters permits the desired frequency response to be specified either numerically (at equally spaced frequencies), graphically, or analytically. Specifications are to be provided also for the permissible 1) resolution and 2) ripple. The ease with which this design method can achieve a specification on frequency response suggests the use of this method whenever the resulting nonrecursive filter can be conveniently implemented on a general-purpose digital computer. Adaptation of these methods to computing power spectra is described.