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Basic units for realization of all-pole and all-zero transfer functions in all-optical systems using ring resonators and electromagnetic-induced transparency (EIT) are introduced. Using the basic blocks for generation of pole and zero proposed Any type and any degree of optical filters and optical processing systems can be implemented. In this paper, z transform is used for design and synthesize of low-pass, bandpass, and high-pass Butterworth optical filters as an example. The stability of optical systems designed by the proposed structures is investigated. In addition, EIT is used for the control of pole and zero position.