7. Conclusions and Future Work

In order to address the problems proposed in the Introduction, this book presented a series of new theoretical results. Firstly, a new theoretical framework was proposed that reformulates the IF neuron encoding of analog signals into spike trains as a problem of uniform sampling. Based on this framework, new algorithms were developed for reconstructing the IF input, under the assumptions that it belongs to a bandlimited space or the more general SIS. Numerical studies were given to show that the new methods have a similar level of accuracy, but are significantly faster than the state-of-the-art algorithms. Secondly, the book has developed two new methodologies for identifying [Nonlinear Filter]-[Ideal IF] and [Linear Filter]-[Leaky IF] circuits. The new methodologies eliminate some of the assumptions of the previous methods, such as that the structure of the filter is known, the filter has fading memory, or that the spiking neuron parameters are known a priori. Numerical simulations were given to show that the identified circuits are adequate representations of the original ones. Thirdly, this book proposed a model consisting of a linear filter whose input and output are encoded into spike trains with two identical IF neurons. An algorithm was subsequently developed that computes directly the output spike times from the input spike times. Numerical simulations were used to show that the new algorithm is significantly faster than the standard approach, involving the reconstruction of the input, simulating the filter and subsequently encoding the resulting output into a spike train.