A novel synthesis method for a class of time-domain passive filters that compensates for waveform distortion caused by frequency dependencies of the transmission properties of signal propagation paths, is formulated. The method is based on the linear response theory and mathematical properties of scattering matrices for passive circuits. This paper focuses on the formulation and theoretical consistency of the method. The causal transfer functions for the filters can be extracted by "regularizing" the inverse of a transfer function of the path. To fulfill the necessary restrictions imposed on the causal functions, regularization is realized by multiplying the function of linear phase filters comprising a sufficient number of resonators by the inverse. The filter circuits are easily derived from the regularized transfer functions through numerical optimization techniques and the coupling matrix synthesis method to determine transmission poles and extract each lumped element value, respectively. The method is then applied to practically designing a filter that compensates for the frequency dependencies of a two-port radio propagation path having a pair of wideband antennas. In addition, applications of the filter and the scope of further developments of this technology are discussed.
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