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We demonstrate the application of optical combs to implement tunable programmable microwave photonic filters. We design well-known multi-tap microwave photonic filters; however, the utilization of an optical comb with a dispersive medium enables scaling of these filters to a large number of taps. We use optical line-by-line pulse shaping to program tap weights, which allows us to shape the filter's bandpass. Our scheme is simple and easily implementable, which provides filters with arbitrary tap weights. As an example, we implement filters with Gaussian apodized tap weights, which achieve more than 35-dB sidelobe suppression. Our experiments provide usable bandwidth, free of sampling spurs, over a Nyquist zone of 5 GHz, equal to half of our 10-GHz comb repetition frequency. Furthermore, we introduce a simple new technique, based on a programmable optical delay line, to uniformly tune the passband …