McClellan Transformations for Multidimensional FIR Digital Filters with Complex Coefficients.

This paper discusses the extension and generalization of McClellan transformation, which is one of the most powerful design methods for two-dimensional (2-D) FIR digital filters, to the multidimensional complex-coefficient FIR digital filter. As the first step, the multidimensional (N-D) analytic signal for the actual signal processing is introduced. Then, the N-D complex-coefficient McClellan transformation is proposed, together with the design method for N-D filters. For the characteristics which are symmetrical in regard to the hyperplane ωi-0 (i-1~N), the N-D analytic signal is used with the frequency components only in the positive ranges of to Then, it suffices to satisfy the filter specifications only in that frequency region, with the characteristics in other regions being arbitrary. In the complex-coefficient McClellan transformation, the complex-coefficient 1-D FIR filter can be used as the fundamental unit, in contrast to the real-coefficient case. This increases the degree of freedom in the filter design, realizing, in general, better characteristics with lower-order transfer functions. Another merit is that the design is simple since the transformation of the variable is employed. As an example, 3-D fan-filter is designed using complex- and real-coefficient McClellan transformations, and the realized characteristics are compared. [ABSTRACT FROM AUTHOR]