Optimum design of discrete-time differentiators via semi-infinite programming approach

In this paper, a general optimum full band high order discrete-time differentiator design problem is formulated as a peak constrained least square optimization problem. That is, the objective of the optimization problem is to minimize the total weighted square error of the magnitude response subject to the peak constraint of the weighted error function. This problem formulation provides a great flexibility for the tradeoff between the ripple energy and the ripple magnitude of the discrete-time differentiator. The optimization problem is actually a semi-infinite programming problem. Our recently developed dual parametrization algorithm is applied for solving the problem. The main advantage of employing the dual parameterization algorithm for solving the problem is the guarantee of the convergence of the algorithm and the obtained solution being the global optimal solution that satisfies the corresponding continuous constraints. Moreover, the computational cost of the algorithm is lower than that of algorithms implementing the semi-definite programming approach

Recent works on optimization for signal processing

This invited presentation has discussed recent works on optimization for signal processing

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

IIR Digital Filter Design Using Convex Optimization

Digital filters play an important role in digital signal processing and communication. From the 1960s, a considerable number of design algorithms have been proposed for finite-duration impulse response (FIR) digital filters and infinite-duration impulse response (IIR) digital filters. Compared with FIR digital filters, IIR digital filters have better approximation capabilities under the same specifications. Nevertheless, due to the presence of the denominator in its rational transfer function, an IIR filter design problem cannot be easily formulated as an equivalent convex optimization problem. Furthermore, for stability, all the poles of an IIR digital filter must be constrained within a stability domain, which, however, is generally nonconvex. Therefore, in practical designs, optimal solutions cannot be definitely attained. In this dissertation, we focus on IIR filter design problems under the weighted least-squares (WLS) and minimax criteria. Convex optimization will be utilized as the major mathematical tool to formulate and analyze such IIR filter design problems. Since the original IIR filter design problem is essentially nonconvex, some approximation and convex relaxation techniques have to be deployed to achieve convex formulations of such design problems. We first consider the stability issue. A sufficient and necessary stability condition is derived from the argument principle. Although the original stability condition is in a nonconvex form, it can be appropriately approximated by a quadratic constraint and readily combined with sequential WLS design procedures. Based on the sufficient and necessary stability condition, this approximate stability constraint can achieve an improved description of the nonconvex stability domain. We also address the nonconvexity issue of minimax design of IIR digital filters. Convex relaxation techniques are applied to obtain relaxed design problems, which are formulated, respectively, as second-order cone programming (SOCP) and semidefinite programming (SDP) problems. By solving these relaxed design problems, we can estimate lower bounds of minimum approximation errors, which are useful in subsequent design procedures to achieve real minimax solutions. Since the relaxed design problems are independent of local information, compared with many prevalent design methods which employ local search, the proposed design methods using the convex relaxation techniques have an increased chance to obtain an optimal design

Precise velocity and acceleration determination using a standalone GPS receiver in real time

Precise velocity and acceleration information is required for many real time applications. A standalone GPS receiver can be used to derive such information; however, there are many unsolved problems in this regard. This thesis establishes the theoretical basis for precise velocity and acceleration determination using a standalone GPS receiver in real time. An intensive investigation has been conducted into the Doppler effect in GPS. A highly accurate Doppler shift one-way observation equation is developed based on a comprehensive error analysis of each contributing factor including relativistic effects. Various error mitigation/elimination methods have been developed to improve the measurement accuracy of both the Doppler and Doppler-rate. Algorithms and formulae are presented to obtain real-time satellite velocity and acceleration in the ECEF system from the broadcast ephemeris. Low order IIR differentiators are designed to derive Doppler and Doppler-rate measurements from the raw GPS data for real-time applications. Abnormalities and their corresponding treatments in real-time operations are also discussed. In addition to the velocity and acceleration determination, this thesis offers a good tool for GPS measurement modelling and for design of interpolators, differentiators, as well as Kalman filters. The relativistic terms presented by this thesis suggest that it is possible to measure the geopotential directly using Doppler shift measurements. This may lead to a foundation for the development of a next generation satellite system for geodesy in the future

Analysis of Nonlinear Behaviors, Design and Control of Sigma Delta Modulators

M PhilSigma delta modulators (SDMs) have been widely applied in analogue-to-digital (A/D) conversion for many years. SDMs are becoming more and more popular in power electronic circuits because it can be viewed and applied as oversampled A/D converters with low resolution quantizers. The basic structure of an SDM under analytical investigation consists of a loop filter and a low bit quantizer connected by a negative feedback loop. Although there are numerous advantages of SDMs over other A/D converters, the application of SDMs is limited by the unboundedness of the system states and their nonlinear behaviors. It was found that complex dynamical behaviors exist in low bit SDMs, and for a bandpass SDM, the state space dynamics can be represented by elliptic fractal patterns confined within two trapezoidal regions. In all, there are three types of nonlinear behaviors, namely fixed point, limit cycle and chaotic behaviors. Related to the unboundedness issue, divergent behavior of system states is also a commonly discovered phenomenon. Consequently, how to design and control the SDM so that the system states are bounded and the unwanted nonlinear behaviors are avoided is a hot research topic worthy of investigated. In our investigation, we perform analysis on such complex behaviors and determine a control strategy to maintain the boundedness of the system states and avoid the occurrence of limit cycle behavior. For the design problem, we impose constraints based on the performance of an SDM and determine an optimal design for the SDM. The results are significantly better than the existing approaches

Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

Space Communications: Theory and Applications. Volume 3: Information Processing and Advanced Techniques. A Bibliography, 1958 - 1963

Annotated bibliography on information processing and advanced communication techniques - theory and applications of space communication