1. Introduction

The elementary computational unit of the brain is the spiking neuron, which generates a sequence of short impulses, or spikes, in response to an analog input. The integrate-and-fire (IF) neuron is a popular model of the spiking neuron, given its significance from a biological as well as an engineering perspective. This chapter introduces the main literature concepts used in this book, and gives motivation for three research problems, given as follows. The first problem consists in developing new mathematical formulations for the encoding and decoding of analog signals using IF neurons. Another important problem that is being addressed in this book is that of inferring cascade models for sensory processing circuits, consisting of filters in series with IF neurons, directly from input-output observations. The third problem considered is the lack of a general theory to characterize the processing of information by circuits that operate with spike trains, or to design circuits that implement particular processing tasks, in a similar fashion to classical analog and digital filters.