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Complex coefficient digital filters, with applications for processing real sequences, are examined. The method is quite general, and allows any real rational transfer function to be expressed in terms of a complex rational transfer function of reduced order. When implemented in complex hardware form, the reduction of filter order can provide an increase in computational efficiency and speed. Conventional filter structures, such as parallel, cascade, lattice, and state-space forms, are extended to the complex domain. Illustrative examples of complex coefficient filter synthesis are included, along with coefficient sensitivity comparisons between the complex coefficient filters and their real coefficient counterparts.