Design of 3-D FIR digital filters using integral squared error criterion and transformation method

In this paper, the design of three-dimensional (3-D) FIR filters using McClellan transform method and integral squared error (ISE) criterion is presented. The 3-D filters with cone-shaped characteristics are considered in the approach. By minimizing the ISE function and double integration, a novel closed-form solution for the transform parameters is developed. The new relations for the transform coefficients are expressed in terms of the desired angle of inclination of the cone. The scaling problem of transformation function is also under discussion, as well as the choice of an appropriate cut-off frequency of the 1-D filter prototype. Several design examples are demonstrated to illustrate the merits of the proposed new technique. Key-Words: Three-dimensional filters, FIR digital filters, McClellan transformation, Integral squared error criterion, Transform parameters, Isopotential contours, Scaled transform function