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A tunable photonic RF signal processor is proposed and demonstrated. The filter structure comprises a reconfigurable Opto-VLSI processor for tunability, arrayed waveguide gratings for wavelength slicing and multiplexing, a custom-made fiber array for wavelength routing and dropping, and high-dispersion fibres for true-time delay generation. The processor structure enables positive and negative weights to be synthesised thus realising arbitrary responses. The proof-of-concept of the tunable photonic RF signal processor is experimentally demonstrated.