Design of FIR digital filters with prescribed flatness and peak error constraints using second-order cone programming

This paper studies the design of digital finite impulse response (FIR) filters with prescribed flatness and peak design error constraints using second-order cone programming (SOCP). SOCP is a powerful convex optimization method, where linear and convex quadratic inequality constraints can readily be incorporated. It is utilized in this study for the optimal minimax and least squares design of linear-phase and low-delay (LD) FIR filters with prescribed magnitude flatness and peak design error. The proposed approach offers more flexibility than traditional maximally-flat approach for the tradeoff between the approximation error and the degree of design freedom. Using these results, new LD specialized filters such as digital differentiators, Hilbert Transformers, Mth band filters and variable digital filters with prescribed magnitude flatness constraints can also be derived. © 2005 IEEE.published_or_final_versio

Design and multiplierless realization of digital synthesis filters for hybrid-filter-bank A/D converters

This paper studies the optimal least squares and minimax design and realization of digital synthesis filters for hybrid-filter-bank analog-to-digltal converters (HFB ADCs) to meet a given spurious-free dynamic range (SFDR). The problem for designing finite-impulse-response synthesis filters is formulated as a second-order cone-programming problem, which is convex and allows linear and quadratic constraints such as peak aliasing error to be incorporated. The fixed coefficients of the designed synthesis filters are efficiently implemented using sum-of-power-of-two (SOPOT) coefficients, while the internal word length used for each intermediate data is minimized using geometric programming. The main sources of error are analyzed, and a new formula of SFDR in terms of these errors is derived. The effects of component variations of analog analysis filters on the HFB ADC are also addressed by means of two new robust HFB ADC design algorithms based on stochastic uncertainty and worst case uncertainty models. Design results show that the proposed approach offers more flexibility and better performance than conventional methods in achieving a given SFDR and that the robust design algorithms are more robust to parameter uncertainties than the nominal design in which the uncertainties are not taken into account. © 2009 IEEE.published_or_final_versio

A new method for designing causal stable IIR variable fractional delay digital filters

This paper studies the design of causal stable Farrow-based infinite-impulse response (IIR) variable fractional delay digital filters (VFDDFs), whose subfilters have a common denominator. This structure has the advantages of reduced implementation complexity and avoiding undesirable transient response when tuning the spectral parameter in the Farrow structure. The design of such IIR VFDDFs is based on a new model reduction technique which is able to incorporate prescribed flatness and peak error constraints to the IIR VFDDF under the second order cone programming framework. Design example is given to demonstrate the effectiveness of the proposed approach. © 2007 IEEE.published_or_final_versio

Design of complex-valued variable digital filters and its application to the realization of arbitrary sampling rate conversion for complex signals

The 47th Midwest Symposium on Circuits and Systems Conference, Salt Lake City, Utah, USA, 25-28 July 2004This paper studies the design of complex-valued variable digital filters (CVDFs) and their applications to the efficient arbitrary sample rate conversion for complex signals in software radio receivers. The design of CVDFs using either the minimax or least squares criteria is formulated as a convex optimization problem and solved using the second order cone programming (SOCP) or semidefmite programming (SDP). In addition, linear and convex quadratic inequality constraints can be readily incorporated. Design examples are given to demonstrate the effectiveness of the proposed approach.published_or_final_versio

Design of multi-plet perfect reconstruction filter banks using frequency-response masking technique

This paper proposes a new design method for a class of two-channel perfect reconstruction (PR) filter banks (FBs) called multi-plet FBs with very sharp cutoff using frequency- response masking (FRM) technique. The multi-plet FBs are PR FBs and their frequency characteristics are controlled by a single subfilter. By recognizing the close relationship between the subfilter and the FRM-based halfband filter, very sharp cutoff PR multi-plet FBs can be realized with reduced implementation complexity. The design procedure is very general and it can be applied to both linear-phase and low-delay PR FBs. Design examples are given to demonstrate the usefulness of the proposed method. © 2008 IEEE.published_or_final_versio

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

Optimization design of mth-band FIR filters with application to image processing

Cone programming (CP) is a class of convex optimization technique, in which a linear objective function is minimized over the intersection of a set of affine constraints. Such constraints could be linear or convex, equalities or inequalities. Owing to its powerful optimization capability as well as flexibility in accommodating various constraints, the cone programming finds wide applications in digital filter design. In this thesis, fundamentals of linear-phase M th-band FIR filters are first introduced, which include the time-domain interpolation condition and the desired frequency specifications. The restriction of the interpolation matrix M for linear-phase two-dimensional (2-D) M th-band filters is also discussed by considering both the interpolation condition and the symmetry of the impulse response of the 2-D filter. Based on the analysis of the M th-band properties, a semidefinite programming (SOP) optimization approach is developed to design linear-phase 1-0 and 2-D M th-band filters. The 2-D SOP optimization design problem is modeled based on both the mini-max and the least-square error criteria. In contrast to the 1-D based design, the 2-D direct SDP design can offer an optimal equiripple result. A second-order cone programming (SOCP) optimization approach is then presented as an alternative for the design of M th-band filters. The performances as well as the design complexity of these two design approaches are justified through numerical design examples. Simulation results show that the performance of the SOCP approach is better than that of the SDP approach for 1-D M th-band filter design due to its reduced computational complexity for the worst-case, whereas the SDP approach is more appropriate for the 2-D M th-band filter design than the SOCP approach because of its efficient and simple optimization structure. Moreover, the designed M th-band filters are proved useful in image interpolation according to both the visual quality and the peak signal-to-noise ratio (PSNR) for the images with different levels of details

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

Exploiting Heterogeneity in Networks of Aerial and Ground Robotic Agents

By taking advantage of complementary communication technologies, distinct sensing functionalities and varied motion dynamics present in a heterogeneous multi-robotic network, it is possible to accomplish a main mission objective by assigning specialized sub-tasks to specific members of a robotic team. An adequate selection of the team members and an effective coordination are some of the challenges to fully exploit the unique capabilities that these types of systems can offer. Motivated by real world applications, we focus on a multi-robotic network consisting off aerial and ground agents which has the potential to provide critical support to humans in complex settings. For instance, aerial robotic relays are capable of transporting small ground mobile sensors to expand the communication range and the situational awareness of first responders in hazardous environments. In the first part of this dissertation, we extend work on manipulation of cable-suspended loads using aerial robots by solving the problem of lifting the cable-suspended load from the ground before proceeding to transport it. Since the suspended load-quadrotor system experiences switching conditions during this critical maneuver, we define a hybrid system and show that it is differentially-flat. This property facilitates the design of a nonlinear controller which tracks a waypoint-based trajectory associated with the discrete states of the hybrid system. In addition, we address the case of unknown payload mass by combining a least-squares estimation method with the designed controller. Second, we focus on the coordination of a heterogeneous team formed by a group of ground mobile sensors and a flying communication router which is deployed to sense areas of interest in a cluttered environment. Using potential field methods, we propose a controller for the coordinated mobility of the team to guarantee inter-robot and obstacle collision avoidance as well as connectivity maintenance among the ground agents while the main goal of sensing is carried out. For the case of the aerial communications relays, we combine antenna diversity with reinforcement learning to dynamically re-locate these relays so that the received signal strength is maintained above a desired threshold. Motivated by the recent interest of combining radio frequency and optical wireless communications, we envision the implementation of an optical link between micro-scale aerial and ground robots. This type of link requires maintaining a sufficient relative transmitter-receiver position for reliable communications. In the third part of this thesis, we tackle this problem. Based on the link model, we define a connectivity cone where a minimum transmission rate is guaranteed. For example, the aerial robot has to track the ground vehicle to stay inside this cone. The control must be robust to noisy measurements. Thus, we use particle filters to obtain a better estimation of the receiver position and we design a control algorithm for the flying robot to enhance the transmission rate. Also, we consider the problem of pairing a ground sensor with an aerial vehicle, both equipped with a hybrid radio-frequency/optical wireless communication system. A challenge is positioning the flying robot within optical range when the sensor location is unknown. Thus, we take advantage of the hybrid communication scheme by developing a control strategy that uses the radio signal to guide the aerial platform to the ground sensor. Once the optical-based signal strength has achieved a certain threshold, the robot hovers within optical range. Finally, we investigate the problem of building an alliance of agents with different skills in order to satisfy the requirements imposed by a given task. We find this alliance, known also as a coalition, by using a bipartite graph in which edges represent the relation between agent capabilities and required resources for task execution. Using this graph, we build a coalition whose total capability resources can satisfy the task resource requirements. Also, we study the heterogeneity of the formed coalition to analyze how it is affected for instance by the amount of capability resources present in the agents