Minimal realizations of direct, parallel, and cascade digital filters are presented. The canonical realizations are developed by assigning circuit elements to represent the computational operations in the difference equations or transfer functions characterizing the digital tutors. The number of circuit elements (adders, multipliers, and delayers), and the number of constants and variables, and arithmetic operations (additions and multiplications) are noted. The costs of the three realizations are compared and systematic procedures for realizing minimal digital filters arc indicated.