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Multipath is a major impairment in a wireless communications environment, and channel estimation algorithms are of interest. We propose a superimposed periodic pilot scheme for finite-impulse response (FIR) channel estimation. A simple first-order statistic is used, and any FIR channel can be estimated. There is no loss of information rate but a controllable increase in transmission power. We derive the variance expression of our linear channel estimate and compare with the Cramer-Rao bound. Numerical examples illustrate the effectiveness of the proposed method.