In this paper, we aim at analyzing the characteristic of neuronal population responses to instantaneous or time-dependent inputs and the role of synapses in neural information processing. We have derived an evolution equation of the membrane potential density function with synaptic depression, and obtain the formulas for analytic computing the response of instantaneous fire rate. Through a technical analysis, we arrive at several significant conclusions: The background inputs play an important role in information processing and act as a switch betwee temporal integration and coincidence detection. the role of synapses can be regarded as a spatio-temporal filter; it is important in neural information processing for the spatial distribution of synapses and the spatial and temporal relation of inputs. The instantaneous input frequency can affect the response amplitude and phase delay.