Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Feedback for neuronal system identification

In order to estimate reliable models from noisy input-output data, system identification techniques usually require that the data be generated by a process with a fading memory. Non-equilibrium systems such as neuronal and chaotic models lack a fading memory. Their identification is challenging, in particular in the presence of input noise. In this thesis, we propose a methodology based on the prediction-error method for the identification of neuronal systems subject to input-additive noise. We build on the fundamental observation that while a neuronal model does not have a fading memory, it can be transformed into a fading memory system by output feedback. Our ideas can be generalized to any non-equilibrium system sharing this property. At the core of the methodology is the use of output feedback in experiment design. We provide a theoretical justification for this design choice, which has been exploited in neurophysiology since the invention of the voltage-clamp experiment. To investigate the problem of feedback for identification, we first address the estimation of simple non-equilibrium systems in Lure form, and show that feedback allows estimating the nonlinearity in a static experiment. We then address the estimation of conductance-based models. Assuming that an informed choice can be made on the elements of the model structure, we show that consistent parameter estimates can be obtained when noise is only present at the system input. Finally, we approach the problem from a black-box perspective, and propose identifying the neuronal internal dynamics using a universal approximator with Generalized Orthogonal Basis Functions.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) – Brasil (Finance Code 001

Wavelets and Subband Coding

First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book