  The spiking neural network (SNN) has been attracting considerable attention
not only as a mathematical model for the brain, but also as an energy-efficient
information processing model for real-world applications. In particular, SNNs
based on temporal coding are expected to be much more efficient than those
based on rate coding, because the former requires substantially fewer spikes to
carry out tasks. As SNNs are continuous-state and continuous-time models, it is
favorable to implement them with analog VLSI circuits. However, the
construction of the entire system with continuous-time analog circuits would be
infeasible when the system size is very large. Therefore, mixed-signal circuits
must be employed, and the time discretization and quantization of the synaptic
weights are necessary. Moreover, the analog VLSI implementation of SNNs
exhibits non-idealities, such as the effects of noise and device mismatches, as
well as other constraints arising from the analog circuit operation. In this
study, we investigated the effects of the time discretization and/or weight
quantization on the performance of SNNs. Furthermore, we elucidated the effects
the lower bound of the membrane potentials and the temporal fluctuation of the
firing threshold. Finally, we propose an optimal approach for the mapping of
mathematical SNN models to analog circuits with discretized time.
