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This letter presents an application of a recently developed coupling matrix synthesis technique to design of coupled-resonator filters with dispersive inter-resonator couplings. This technique is used to design a novel coupled-cavity bandpass filter. Measurements validate the design and confirm effectiveness of the synthesis method. The filter is a four-pole generalized Chebyshev filter with three transmission zeros. Resonators are arranged in a quadruplet configuration and employ a single dispersive cross coupling to produce an extra zero in comparison to classical approaches. Frequency-dependent coupling was realized via a rectangular waveguide iris with an incomplete height conducting post.