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A novel approach consisting of discrete signal processing (DSP) technique and optimization method is developed to implement a second-order differentiator at microwave frequencies. To utilize the transfer function of a second-order differentiator developed in the DSP study, we formulate the chain scattering parameters of transmission lines in the Z domain. In particular, it is shown that shunt stubs combining with nonuniform serial lines lead to the realization of a second-order microwave differentiator. Some examples are presented to illustrate the validity of this approach.