Design of FIR digital filters using prescribed subfilters

A method for the design of linear-phase digital filters by the tapped cascaded interconnection of identical subfilters is presented. The method is an extension of the method proposed by Saramaki (1987). An example is given to show that the number of distinct multipliers of the filter determined by the proposed method is less than that of filters determined by Saramaki's method (1987). We also consider the case in which the subfilters are determined by multiple use of a single filter. In particular, if we can make the subfilters multiplierless then the number or multiplications per sample required to implement the overall filter is less than that required by the direct-form minimax method. Methods for the design of computationally efficient filters are also developed based on the proposed transformation method. The multiplication rate of the overall filter is the same as that of the prototype filter. It is very low as compared to that designed by the equivalent direct-form minimax method. With the proposed transformation method, methods for the design of a filter having nth-order tangency at both ends (0, π) are also developed. This is an extension of Vaidynathan's method (1985) and the proposed transformation method. The advantages of the method are that the resulting filters have very flat passbands and the stopbands are computationally efficient.