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For the first time, a systematic synthesis method for cross-coupled dispersive delay structures (DDSs) with controlled magnitude for analog signal processing applications is proposed. In this method, the transfer function is synthesized using a polynomial expansion approach, which allows to separately control the magnitude and group-delay response of the DDS. The synthesized transfer function also features a reduced order-namely, half-compared to that of previously reported synthesis techniques for linear-phase filters. Once it has been constructed, the transfer function is transferred into coupling matrices that can be implemented in arbitrary cross-coupled-resonator technologies. Several design examples are provided for different prescribed group-delay responses. An experimental waveguide prototype is demonstrated. The agreement between the measured and prescribed responses illustrates the proposed synthesis method.