This paper studies synchronization phenomena of spike-trains and approximation of target spike-trains in a simple network of digital spiking neurons. Repeating integrate-and-fire behavior between a periodic base signal and constant firing threshold, the neurons can generate various spike-trains. Connecting multiple neurons by cross-firing with delay, the network is constructed. The network can exhibit multi-phase synchronization of various spike-trains. Stability of the synchronization phenomena can be guaranteed theoretically. Applying a simple winner-take-all switching, the network can approximate target spike-trains automatically. In order to evaluate the approximation performance, we present two metrics: spike-position error and spike missing rate. Using the metrics, approximation capability of the network is investigated in typical target signals. Presenting an FPGA based hardware prototype, typical synchronization phenomenon and spike-train approximation are confirmed experimentally.

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