Digital filters having sharp transition band play a vital role in modern digital signal processing (DSP) applications. Emerging technologies require digital filters to be both computationally efficient in software/hardware realizations. This thesis is concerned with the design and structural-level optimization of sharp transition band digital filters employing the well known frequency response masking (FRM) approach. Unlike the conventional finite impulse response (FIR) based FRM approach, the FRM technique used in this thesis incorporates infinite impulse response (IIR) digital interpolation subfilters, thereby reducing the overall filter order that results in a reduction of hardware complexity. Two realization methods are discussed in this thesis, namely, the bilinear-lossless-discrete-integrators (bilinear-LDI) digital filter design technique, and the lattice wave digital filter (lattice WDF) digital filter design technique. Diversity controlled (DC) genetic algorithm (GA) is employed to optimize both types of IIR based FRM digital filters over the efficient canonical signed digit (CSD) multiplier coefficient space. DCGAs represent FRM digital filters by a binary chromosome and proceed from a population pool of candidate chromosomes to future generations in order to arrive at the desired FRM digital filter satisfying the design specifications. A novel cost-function is used that allows the DCGA to simultaneously optimize both the amplitude-frequency and group-delay frequency response. A fast convergence speed has been observed. / Communications

Recently, many identity-based two-party and three-party key agreement schemes were proposed based on pairing cryptosystems. Multi-party (including more than three parties) key agreement protocols, which are called conference key schemes, can be applied to distributed systems and wireless environments such as Ad hoc networks. However, it is not easy to extend two or three-party schemes to multi-party ones with the guarantee of efficiency and security. In addition to the above two properties, inter-domain environments should also be considered in identity-based key agreement systems. However, only few identity-based multi-party conference key agreement schemes in single domain were proposed in the literature and they did not satisfy all of the security attributes such as forward secrecy and withstanding impersonation. In this thesis, we will propose a novel efficient single-domain identity-based multi-party conference key scheme and extend it to an inter-domain version. Finally, we will prove that the proposed schemes satisfy the required security attributes via formal methods.

This thesis concerns modeling and control of bilinear systems (BLS). BLS are linear but not jointly linear in state and control. In the first part of the thesis, a background to BLS and their applications to modeling and control is given. The second part, and likewise the principal theme of this thesis, is dedicated to theoretical aspects of identification, modeling and control of mainly BLS, but also linear systems. In the last part of the thesis, applications of bilinear and linear modeling and control to the activated sludge process (ASP) are given.

Solution methodologies for mixed integer bilinear problems (MIBLP) are studied in this dissertation. This problem class is motivated using the pooling problem, a multicommodity network flow problem that typically arises in chemical engineering applications. Stronger than previously known results are provided to compare the strengths of polyhedral relaxations of the pooling problem. A novel single node flow relaxation, defined by a bilinear equality constraint and flow balance, is proposed for the pooling problem. Linear valid inequalities in the original space of variables are derived using a well-known technique called lifting. Mixed integer linear (MILP) formulations are proposed for generating feasible solutions to the pooling problem. Some of these MILP models arise from variable discretizations while others possess a network flow interpretation. The effectiveness of these MILP models is empirically validated on a library of medium and large-scale instances. General MIBLPs, not necessarily pooling problems, are solved using extended MILP reformulations. The reformulation is obtained by writing binary representation for each general integer variable. Facet-defining inequalities are provided for the reformulation of each bilinear term. New valid inequalities are also proposed for bilinear terms with a nontrivial upper bound. The proposed reformulation and cutting planes are compared against a global solver on five different classes of MIBLPs.

The Empirical Likelihood method (ELM) was introduced by A. B. Owen to test hypotheses in the early 1990s. It's a nonparametric method and uses the data directly to do statistical tests and to compute confidence intervals/regions. Because of its distribution free property and generality, it has been studied extensively and employed widely in statistical topics. There are many classical test statistics such as the Cramer-von Mises (CM) test statistic, the Anderson-Darling test statistic, and the Watson test statistic, to name a few. However, none is universally most powerful. This thesis is dedicated to extending the ELM to several interesting statistical topics in hypothesis tests. First of all, we focus on testing the fit of distributions. Based on the CM test, we propose a novel Jackknife Empirical Likelihood test via estimating equations in testing the goodness-of-fit. The proposed new test allows one to add more relevant constraints so as to improve the power. Also, this idea can be generalized to other classical test statistics. Second, when aiming at testing the error distributions generated from a statistical model (e.g., the regression model), we introduce the Jackknife Empirical Likelihood idea to the regression model, and further compute the confidence regions with the merits of distribution free limiting chi-square property. Third, the ELM based on some weighted score equations are proposed for constructing confidence intervals for the coefficient in the simple bilinear model. The effectiveness of all presented methods are demonstrated by some extensive simulation studies.

Low-sensitivity switched capacitor filters imitating 'R','L' and 'C' can be built by means of capacitances, ordinary switches and voltage inverter switches (VIS). These structures carry the inherent bilinear transformation of their doubly resistively terminated ladder reference filters. This one to one correspondence between the 's-domain' and the 'z-domain' results in the Nyquist criterion being the only limitation on the sampling frequency. This eliminates the necessity for oversampling and VIS filters can be designed for high operating rates. Filters based on VIS principle were analysed in previous literatures in the 'phi-domain'. In this thesis work, a successful attempt has been made to formulate an analysis procedure for discrete-time filters based on VIS principle in the 'z-domain'. Significant details have been brought out in comparison with the respective reference filter. A fifth-order lowpass filter has been designed and implemented to exhibit the closeness to the bilinearly transformed continuous-time reference filter. Settling time analysis has been done to justify the need for filters using VIS principle as compared to the filters employing integrator based switched capacitor filter. It is shown that VIS filter can be made to settle within half the period required for a conventional integrator based switched capacitor filter.

In a multi-receiver encryption environment, a sender can randomly choose a set of authorized receivers while distributing messages to them efficiently and securely. Recently, more and more researchers concern the privacy of receivers. They mentioned that an authorized receiver does not want other entities, except the service provider, to be able to derive her/his identity in many applications such as pay-TV. However, most of these protocols either provide no formal security proofs or are inefficient owing to high computation cost. In this thesis, we construct two provably secure and efficient anonymous multi-receiver certificated-based encryption schemes, PMCE and SCMCE, which avoid the key escrow problem while preserving the implicit certification of identity-based setting. The proposed PMCE and SCMCE get rid of pairing computation to encrypt a message and only need one and two pairing computations to decrypt the ciphertext, respectively. Finally, we define the security models and offer formal proofs to all properties including receiver anonymity.

Cloud computing has been developed rapidly in recent years, and offers novel concepts and innovations in computer use. One application of cloud computing is that people can designate a proxy to help them to execute a number of tasks in certain situations instead of undertaking all tasks themselves. With this application, people can benefit from the proxy; however, some information is revealed to the proxy, such as their activities, and private data. That is, the proxy is aware of the actions of people through delegation processes, and proxy re-encryption which is a cryptographic primitive has been proposed to solve this problem. In the proxy re-encryption system, when a user (e.g., Alice) wants to send a ciphertext that is encrypted by her secret key and stored in the cloud to another user (e.g., Bob), she can designate a proxy to transform the ciphertext into a different ciphertext that can be decrypted by Bob¡¦s private key. Based on attribute-based encryption and proxy re-encryption, we propose attribute-based proxy re-encryption with bilinear pairing. Furthermore, in the proposed scheme, third paries cannot decrypt the ciphertext if they do no have matching attributes, regardless of being helped by proxy. Finally, we offer security proofs to demonstrate that the proposed scheme satisfies the essential requirements of attribute-based encryption schemes and proxy re-encryption schemes.

Novel methods of system identification are developed in this dissertation. First set of methods are designed to realize time varying linear dynamical system models from input-output experimental data. The preliminary results obtained in a recent paper by the author are extended to establish a new algorithm called the Time Varying Eigensystem Realization Algorithm (TVERA). The central aim of this algorithm is to obtain a linear, time varying, discrete time model sequence of the dynamic system directly from the input-output data. Important results relating to concepts concerning coordinate systems for linear time varying systems are developed (discrete time theory) and an intuitive understanding of equivalent realizations is provided. A procedure to develop first few time step models is detailed, providing a unified solution to the time varying identification problem. The practical problem of identifying the time varying generalized Markov parameters required for TVERA is presented as the next result. In the process, we generalize the classical time invariant input output AutoRegressive model with an eXogenous input (ARX) models to the time varying case and realize an asymptotically stable observer as a byproduct of the calculations. It is further found that the choice of the generalized time varying ARX model (GTV-ARX) can be set to realize a time varying dead beat observer. Methods to use the developed algorithm(s) in this research are then considered for application to the identification of system models that are bilinear in nature. The fact that bilinear plant models become linear for constant inputs is used in the development of an algorithm that generalizes the classical developments of Juang. An intercept problem is considered as a candidate for application of the time varying identification scheme, where departure motion dynamics model sequence is calculated about a nominal trajectory with suboptimal performance owing to the presence of unstructured perturbations. Control application is subsequently demonstrated. The dynamics of a particle in a rotating tube is considered next for identification using the time varying eigensystem realization algorithm. Continuous time bilinear system identification method is demonstrated using the particle example and the identification of an automobile brake model.

In this thesis a stepped-frequency Inverse Synthetic Aperture Radar (ISAR) is employed to develop two-dimensional range-Doppler images of a small ghter aircraft which exhibits three dimensional rotational rotation. The simulation is designed such that the target can exhibit yaw, pitch and roll motions at the same time. First, radar returns from prominent scatterers of various parts of the target are processed and displayed using conventional Fourier transform. The eects of dierent complex motion types and scenarios are observed and discussed. Then, several linear and bi-linear time-frequency distributions including shorttime Fourier transform, Wigner-Ville, pseudo Wigner-Ville, smoothed pseudo Wigner-Ville, Choi-Williams, Born-Jordan and Zhao-Atlas-Marks distributions are applied to the same target and scenarios. The performance of the transforms is compared for each scenario. The reasons for success of the distributions are discussed thoroughly.