Developing neuromorphic computing paradigms that mimic nervous system function is an emerging field of research with high potential for technical applications. In the present study we take inspiration from the cricket auditory system and propose a biologically plausible neural network architecture that can explain how acoustic pattern recognition is achieved in the cricket central brain. Our circuit model combines two key features of neural processing dynamics: Spike Frequency Adaptation (SFA) and synaptic short term plasticity. We developed and extensively tested the model function in software simulations. Furthermore, the feasibility of an analogue VLSI implementation is demonstrated using a multi-neuron chip comprising Integrate-and-Fire (IF) neurons and adaptive synapses.