Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Sampling from a system-theoretic viewpoint

This paper studies a system-theoretic approach to the problem of reconstructing an analog signal from its samples. The idea, borrowed from earlier treatments in the control literature, is to address the problem as a hybrid model-matching problem in which performance is measured by system norms. \ud \ud The paper is split into three parts. In Part I we present the paradigm and revise the lifting technique, which is our main technical tool. In Part II optimal samplers and holds are designed for various analog signal reconstruction problems. In some cases one component is fixed while the remaining are designed, in other cases all three components are designed simultaneously. No causality requirements are imposed in Part II, which allows to use frequency domain arguments, in particular the lifted frequency response as introduced in Part I. In Part III the main emphasis is placed on a systematic incorporation of causality constraints into the optimal design of reconstructors. We consider reconstruction problems, in which the sampling (acquisition) device is given and the performance is measured by the $L^2$-norm of the reconstruction error. The problem is solved under the constraint that the optimal reconstructor is $l$-causal for a given $l\geq 0,$ i.e., that its impulse response is zero in the time interval $(-\infty,-l h),$ where $h$ is the sampling period. We derive a closed-form state-space solution of the problem, which is based on the spectral factorization of a rational transfer function

Dimension reduction for systems with slow relaxation

We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal' model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.Comment: 48 Pages, 13 figures. Paper dedicated to the memory of Leo Kadanof

Distributed Probabilistic Synchronization Algorithms for Communication Networks

In this paper, we present a probabilistic synchronization algorithm whose convergence properties are examined using tools of rowstochastic matrices. The proposed algorithm is particularly well suited for wireless sensor network applications, where connectivity is not guaranteed at all times, and energy efficiency is an important design consideration. The tradeoff between the convergence speed and the energy use is studied

Signal estimation using H [infinity sign] criteria

In many signal processing and communication (SPC) applications we require to estimate signal corrupted by channel and additive noise. Optimal linear filters and predictors are used to recover signal from given observed (corrupted) signal. Kalman and Wiener filters are commonly used as optimal filters. These filters minimize the mean square error (MSE) or variance of the output error. The minimization require exact knowledge of input signal and noise power spectral density (PSD). Therefore, the performance of Kalman or Wiener filters degrade if the input signal and noise statistics is changing with time and is not known a priori. In many SPC applications there is no exact knowledge of the input signal and noise Statistics and Probability; One solution to this is to use the filters which minimizes MSE and adapt to changing input signals and noise Statistics and Probability; This solution falls into a general category of adaptive filters. Often, convergence speed of the adaptive filter algorithm determines the performance as it is assumed that the convergence speed is fast enough to track the changes in the input signal and noise Statistics and Probability; If the convergence speed is not able to track the input signal and noise statistics one can expect large variation in the output error power. Another approach to overcome unknown input signal and noise statistics is to use the mini-max estimation. One approach towards mini-max estimation is to minimize the error using H[infinity] criteria to obtain H[infinity] filters. This will lead to a conservative (minimize over the worst case input signals) design that is more robust to changes in the input signal and noise Statistics and Probability;;In this dissertation, interpretation of H[infinity] filters for zero mean stationary signals is discussed. From this H[infinity] filters are represented in the time and frequency domain. Performance benefits of H[infinity] filters over minimum variance filters are derived from this representation. Mathematical solutions to compute sub-optimal H[infinity] filters in time and frequency domain are discussed. Finally, performance benefits of H[infinity] filters for the code division multiple access (CDMA) system, signal estimation problems, and adaptive filters are shown through simulation results

Models of statistical self-similarity for signal and image synthesis

Statistical self-similarity of random processes in continuous-domains is defined through invariance of their statistics to time or spatial scaling. In discrete-time, scaling by an arbitrary factor of signals can be accomplished through frequency warping, and statistical self-similarity is defined by the discrete-time continuous-dilation scaling operation. Unlike other self-similarity models mostly relying on characteristics of continuous self-similarity other than scaling, this model provides a way to express discrete-time statistical self-similarity using scaling of discrete-time signals. This dissertation studies the discrete-time self-similarity model based on the new scaling operation, and develops its properties, which reveals relations with other models. Furthermore, it also presents a new self-similarity definition for discrete-time vector processes, and demonstrates synthesis examples for multi-channel network traffic. In two-dimensional spaces, self-similar random fields are of interest in various areas of image processing, since they fit certain types of natural patterns and textures very well. Current treatments of self-similarity in continuous two-dimensional space use a definition that is a direct extension of the 1-D definition. However, most of current discrete-space two-dimensional approaches do not consider scaling but instead are based on ad hoc formulations, for example, digitizing continuous random fields such as fractional Brownian motion. The dissertation demonstrates that the current statistical self-similarity definition in continuous-space is restrictive, and provides an alternative, more general definition. It also provides a formalism for discrete-space statistical self-similarity that depends on a new scaling operator for discrete images. Within the new framework, it is possible to synthesize a wider class of discrete-space self-similar random fields

Generalized linear-in-parameter models : theory and audio signal processing applications

This thesis presents a mathematically oriented perspective to some basic concepts of digital signal processing. A general framework for the development of alternative signal and system representations is attained by defining a generalized linear-in-parameter model (GLM) configuration. The GLM provides a direct view into the origins of many familiar methods in signal processing, implying a variety of generalizations, and it serves as a natural introduction to rational orthonormal model structures. In particular, the conventional division between finite impulse response (FIR) and infinite impulse response (IIR) filtering methods is reconsidered. The latter part of the thesis consists of audio oriented case studies, including loudspeaker equalization, musical instrument body modeling, and room response modeling. The proposed collection of IIR filter design techniques is submitted to challenging modeling tasks. The most important practical contribution of this thesis is the introduction of a procedure for the optimization of rational orthonormal filter structures, called the BU-method. More generally, the BU-method and its variants, including the (complex) warped extension, the (C)WBU-method, can be consider as entirely new IIR filter design strategies.reviewe