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A novel method of rapidly composing any required signal delay or combination of delays from a set of precise fixed delay lines is described. Both simple delays and recirculating delay loops can be obtained. The construction of programmable ring resonators with both optical and electrical delay lines is demonstrated. Tunable comb filters with bandwidths up to 1 GHz were obtained. Since delays can be altered within nanoseconds, many applications in digital and analog signal processing can be realized.