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

The Application of LQG Balanced Truncation Algorithm to the Digital Filter Design Problem

This paper presents a method for using a model reduction algorithm to design low-order digital filters. Designing an IIR digital filter that meets the specifications often leads to a high-order digital filter. To reduce the computation time and increase the response rate of the filter, we need to reduce the order of the high-order digital filter. Applying the LQG balanced truncation algorithm to reduce the demand for high-order digital filters shows that low-order filters can completely replace high-order digital filters. The simulation results show that the use of the LQG balanced truncation algorithm in order to reduce the filter order is correct and efficient

Passivity enforcement for descriptor systems via matrix pencil perturbation

Passivity is an important property of circuits and systems to guarantee stable global simulation. Nonetheless, nonpassive models may result from passive underlying structures due to numerical or measurement error/inaccuracy. A postprocessing passivity enforcement algorithm is therefore desirable to perturb the model to be passive under a controlled error. However, previous literature only reports such passivity enforcement algorithms for pole-residue models and regular systems (RSs). In this paper, passivity enforcement algorithms for descriptor systems (DSs, a superset of RSs) with possibly singular direct term (specifically, D+D T or I-DD T) are proposed. The proposed algorithms cover all kinds of state-space models (RSs or DSs, with direct terms being singular or nonsingular, in the immittance or scattering representation) and thus have a much wider application scope than existing algorithms. The passivity enforcement is reduced to two standard optimization problems that can be solved efficiently. The objective functions in both optimization problems are the error functions, hence perturbed models with adequate accuracy can be obtained. Numerical examples then verify the efficiency and robustness of the proposed algorithms. © 2012 IEEE.published_or_final_versio

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Theoretical and practical aspects of linear and nonlinear model order reduction techniques

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 133-142).Model order reduction methods have proved to be an important technique for accelerating time-domain simulation in a variety of computer-aided design tools. In this study we present several new techniques for model reduction of the large-scale linear and nonlinear systems. First, we present a method for nonlinear system reduction based on a combination of the trajectory piecewise-linear (TPWL) method with truncated-balanced realizations (TBR). We analyze the stability characteristics of this combined method using perturbation theory. Second, we describe a linear reduction method that approximates TBR model reduction and takes advantage of sparsity of the system matrices or available accelerated solvers. This method is based on AISIAD (approximate implicit subspace iteration with alternate directions) and uses low-rank approximations of a system's gramians. This method is shown to be advantageous over the common approach of independently approximating the controllability and observability gramians, as such independent approximation methods can be inefficient when the gramians do not share a common dominant eigenspace. Third, we present a graph-based method for reduction of parameterized RC circuits. We prove that this method preserves stability and passivity of the models for nominal reduction. We present computational results for large collections of nominal and parameter-dependent circuits. Finally, we present a case study of model reduction applied to electroosmotic flow of a marker concentration pulse in a U-shaped microfluidic channel, where the marker flow in the channel is described by a three-dimensional convection-diffusion equation. First, we demonstrate the effectiveness of the modified AISIAD method in generating a low order models that correctly describe the dispersion of the marker in the linear case; that is, for the case of concentration-independent mobility and diffusion constants.(cont) Next, we describe several methods for nonlinear model reduction when the diffusion and mobility constants become concentration-dependent.by Dmitry Missiuro Vasilyev.Ph.D

Passivity check of S-Parameter descriptor systems via S-Parameter generalized hamiltonian methods

This paper extends the generalized Hamiltonian method (GHM) (Zhang , 2009; Zhang and Wong, 2010) and its half-size variant (HGHM) (Zhang and Wong, 2010) to their S-parameter counterparts (called S-GHM and S-HGHM, respectively), for testing the passivity of S-parameter descriptor-form models widely used in high-speed circuit and electromagnetic simulations. The proposed methods are capable of accurately detecting the possible nonpassive regions of descriptor-form models with either scattering or hybrid (impedance or admittance) transfer matrices. Their effectiveness and accuracy are verified with several practical examples. The S-GHM and S-HGHM methods presented here provide a foundation for the passivity enforcement of $S$- parameter descriptor systems. © 2006 IEEE.published_or_final_versio

Reduction of network models with a large number of sources

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Low complexity and efficient dynamic spectrum learning and tunable bandwidth access for heterogeneous decentralized cognitive radio networks

International audienceThis paper deals with the design of the low complexity and efficient dynamic spectrum learning and access (DSLA) scheme for next-generation heterogeneous decentralized Cognitive Radio Networks (CRNs) such as Long Term Evolution-Advanced and 5G. Existing DSLA schemes for decentralized CRNs are focused predominantly on the decision making policies which perform the task of orthogonalization of secondary users to optimum vacant subbands of fixed bandwidth. The focus of this paper is the design of DSLA scheme for decentralized CRNs to support the tunable vacant bandwidth requirements of the secondary users while minimizing the computationally intensive subband switchings. We first propose a new low complexity VDF which is designed by modifying second order frequency transformation and subsequently combining it with the interpolation technique. It is referred to as Interpolation and Modified Frequency Transformation based VDF (IMFT-VDF) and it provides tunable bandpass responses anywhere over Nyquist band with complete control over the bandwidth as well as the center frequency. Second, we propose a tunable decision making policy, ρt_randρt_rand, consisting of learning and access unit, and is designed to take full advantage of exclusive frequency response control offered by IMFT-VDF. The simulation results verify the superiority of the proposed DSLA scheme over the existing DSLA schemes while complexity comparisons indicate total gate count savings from 11% to as high as 87% over various existing schemes. Also, lower number of subband switchings make the proposed scheme power-efficient and suitable for battery-operated cognitive radio terminals