An Architectural Framework for VLSI Time-Recursive Computation with Applications

The time-recursive computation model has been proven as a particularly useful tool in audio, video, radar and sonar real- time data processing architectures. Unlike the FFT based architectures, the time-recursive ones require only local communication, they imply linear implementation cost and they operate in a single-input multiple-output (SIMO) manner. This is appropriate for the above applications since the data are supplied serially. Also, the time-recursive architectures are modular and regular and they allow high degree of parallelism; thus they are very appropriate for VLSI implementation.In this dissertation, we establish an architectural framework for parallel time-recursive computation. We consider a class of linear operators (or signal transformers) that are characterized by discrete time, time invariant, compactly supported, but otherwise arbitrary kernel functions. We specify the properties of linear operators that can be implemented efficiently in a time-recursive way. Based on these properties, we develop a systematic routine that produces a time-recursive architectural implementation for a given operator. We demonstrate the use and effectiveness of this routine by means of specific examples, namely the Discrete Cosine Transform (DCT), the Discrete Fourier Transform (DFT) and the Discrete Wavelet Transform (DWT).By using this architectural framework we obtain novel architectures for the uniform-DFT QMF bank, the cosine modulated QMF bank, the 1-D and 2-D Modulated Lapped Transform (MLT), as well as an Extended Lapped Transform (ELT). Furthermore, the architectural implementation of the Cepstral Transform and a Short Time Fourier Transform are considered based on the time-recursive architecture of the DFT. All of the above designs are modular, regular, with local communication and linear cost in operator counts. In particular, the 1-D MLT requires 1N + 3 adders and N - 1 rotation circuits, where N denotes the data block size. The 2-D MLT requires 3 1-D MLT circuits and no matrix transposition. The ELT has basis length equal to 4N and it requires 3N + 4 multipliers, 4N + 4 adders and N + 2 rotation circuits. These results are expected to have a significant impact on real-time audio and video data compression, in frequency domain adaptive filtering and in spectrum analysis

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Computability and analysis: the legacy of Alan Turing

We discuss the legacy of Alan Turing and his impact on computability and analysis.Comment: 49 page

Error-constrained filtering for a class of nonlinear time-varying delay systems with non-gaussian noises

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this technical note, the quadratic error-constrained filtering problem is formulated and investigated for discrete time-varying nonlinear systems with state delays and non-Gaussian noises. Both the Lipschitz-like and ellipsoid-bounded nonlinearities are considered. The non-Gaussian noises are assumed to be unknown, bounded, and confined to specified ellipsoidal sets. The aim of the addressed filtering problem is to develop a recursive algorithm based on the semi-definite programme method such that, for the admissible time-delays, nonlinear parameters and external bounded noise disturbances, the quadratic estimation error is not more than a certain optimized upper bound at every time step. The filter parameters are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programme method. A simulation example is exploited to illustrate the effectiveness of the proposed design procedures.This work was supported in part by the Leverhulme Trust of the U.K., the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grant 61028008 and Grant 61074016, the Shanghai Natural Science Foundation of China under Grant 10ZR1421200, and the Alexander von Humboldt Foundation of Germany. Recommended by Associate Editor E. Fabre

Robust H-infinity finite-horizon control for a class of stochastic nonlinear time-varying systems subject to sensor and actuator saturations

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This technical note addresses the robust H∞ finite-horizon output feedback control problem for a class of uncertain discrete stochastic nonlinear time-varying systems with both sensor and actuator saturations. In the system under investigation, all the system parameters are allowed to be time-varying, the parameter uncertainties are assumed to be of the polytopic type, and the stochastic nonlinearities are described by statistical means which can cover several classes of well-studied nonlinearities. The purpose of the problem addressed is to design an output feedback controller, over a given finite-horizon, such that the H∞ disturbance attenuation level is guaranteed for the nonlinear stochastic polytopic system in the presence of saturated sensor and actuator outputs. Sufficient conditions are first established for the robust H∞ performance through intensive stochastic analysis, and then a recursive linear matrix inequality (RLMI) approach is employed to design the desired output feedback controller achieving the prescribed H∞ disturbance rejection level. Simulation results demonstrate the effectiveness of the developed controller design scheme.This work was supported under Australian Research Council’s Discovery Projects funding scheme (project DP0880494) and by the German Science Foundation (DFG) within the priority programme 1305: Control Theory of Digitally Networked Dynamical Systems. Recommended by Associate Editor H. Ito