Academic literature on the topic 'Bandwidth matrix'

Polarimetric systems design has seen recent utilization of linear systems theory for system descriptions. Although noise optimal systems have been shown, bandwidth performance has not been addressed in depth generally and is particularly lacking for Mueller matrix (active) polarimetric systems. Bandwidth must be considered in a systematic way for remote sensing polarimetric systems design. The systematic approach facilitates both understanding of fundamental constraints and design of higher bandwidth polarimetric systems. Fundamental bandwidth constraints result in production of polarimetric "artifacts" due to channel crosstalk upon Mueller matrix reconstruction. This dissertation analyzes bandwidth trade-offs in spatio-temporal channeled Mueller matrix polarimetric systems. Bandwidth is directly related to the geometric positioning of channels in the Fourier (channel) space, however channel positioning for polarimetric systems is constrained both physically and by design parameters like domain separability. We present the physical channel constraints and the constraints imposed when the carriers are separable between space and time. Polarimetric systems are also constrained by noise performance, and there is a trade-off between noise performance and bandwidth. I develop cost functions which account for the trade-off between noise and bandwidth for spatio-temporal polarimetric systems. The cost functions allow a systems designer to jointly optimize systems with good bandwidth and noise performance. Optimization is implemented for a candidate spatio-temporal system design, and high temporal bandwidth systems resulting from the optimization are presented. Systematic errors which impact the bandwidth performance and mitigation strategies for these systematic errors are also presented. Finally, a portable imaging Mueller matrix system is built and analyzed based on the theoretical bandwidth analysis and system bandwidth optimization. Temporal bandwidth performance is improved by 300% over a conventional dual rotating retarder Mueller matrix polarimeter. Reconstruction results from the physical instrument are presented, and issues with the implemented system design are discussed.

Dans ce travail, l'approche non-paramétrique par noyaux associés mixtes multivariés est présentée pour les fonctions de densités, de masse de probabilité et de régressions à supports partiellement ou totalement discrets et continus. Pour cela, quelques aspects essentiels des notions d'estimation par noyaux continus (dits classiques) multivariés et par noyaux associés univariés (discrets et continus) sont d'abord rappelés. Les problèmes de supports sont alors révisés ainsi qu'une résolution des effets de bords dans les cas des noyaux associés univariés. Le noyau associé multivarié est ensuite défini et une méthode de leur construction dite mode-dispersion multivarié est proposée. Il s'ensuit une illustration dans le cas continu utilisant le noyau bêta bivarié avec ou sans structure de corrélation de type Sarmanov. Les propriétés des estimateurs telles que les biais, les variances et les erreurs quadratiques moyennes sont également étudiées. Un algorithme de réduction du biais est alors proposé et illustré sur ce même noyau avec structure de corrélation. Des études par simulations et applications avec le noyau bêta bivarié avec structure de corrélation sont aussi présentées. Trois formes de matrices des fenêtres, à savoir, pleine, Scott et diagonale, y sont utilisées puis leurs performances relatives sont discutées. De plus, des noyaux associés multiples ont été efficaces dans le cadre de l'analyse discriminante. Pour cela, on a utilisé les noyaux univariés binomial, catégoriel, triangulaire discret, gamma et bêta. Par la suite, les noyaux associés avec ou sans structure de corrélation ont été étudiés dans le cadre de la régression multiple. En plus des noyaux univariés ci-dessus, les noyaux bivariés avec ou sans structure de corrélation ont été aussi pris en compte. Les études par simulations montrent l'importance et les bonnes performances du choix des noyaux associés multivariés à matrice de lissage pleine ou diagonale. Puis, les noyaux associés continus et discrets sont combinés pour définir les noyaux associés mixtes univariés. Les travaux ont aussi donné lieu à la création d'un package R pour l'estimation de fonctions univariés de densités, de masse de probabilité et de régression. Plusieurs méthodes de sélections de fenêtres optimales y sont implémentées avec une interface facile d'utilisation. Tout au long de ce travail, la sélection des matrices de lissage se fait généralement par validation croisée et parfois par les méthodes bayésiennes. Enfin, des compléments sur les constantes de normalisations des estimateurs à noyaux associés des fonctions de densité et de masse de probabilité sont présentés<br>This work is about nonparametric approach using multivariate mixed associated kernels for densities, probability mass functions and regressions estimation having supports partially or totally discrete and continuous. Some key aspects of kernel estimation using multivariate continuous (classical) and (discrete and continuous) univariate associated kernels are recalled. Problem of supports are also revised as well as a resolution of boundary effects for univariate associated kernels. The multivariate associated kernel is then defined and a construction by multivariate mode-dispersion method is provided. This leads to an illustration on the bivariate beta kernel with Sarmanov's correlation structure in continuous case. Properties of these estimators are studied, such as the bias, variances and mean squared errors. An algorithm for reducing the bias is proposed and illustrated on this bivariate beta kernel. Simulations studies and applications are then performed with bivariate beta kernel. Three types of bandwidth matrices, namely, full, Scott and diagonal are used. Furthermore, appropriated multiple associated kernels are used in a practical discriminant analysis task. These are the binomial, categorical, discrete triangular, gamma and beta. Thereafter, associated kernels with or without correlation structure are used in multiple regression. In addition to the previous univariate associated kernels, bivariate beta kernels with or without correlation structure are taken into account. Simulations studies show the performance of the choice of associated kernels with full or diagonal bandwidth matrices. Then, (discrete and continuous) associated kernels are combined to define mixed univariate associated kernels. Using the tools of unification of discrete and continuous analysis, the properties of the mixed associated kernel estimators are shown. This is followed by an R package, created in univariate case, for densities, probability mass functions and regressions estimations. Several smoothing parameter selections are implemented via an easy-to-use interface. Throughout the paper, bandwidth matrix selections are generally obtained using cross-validation and sometimes Bayesian methods. Finally, some additionnal informations on normalizing constants of associated kernel estimators are presented for densities or probability mass functions

碩士<br>國立中央大學<br>電機工程研究所<br>99<br>In this thesis, compact Wilkinson power divider and Butler matrix are designed with no bandwidth reduction. Traditional Wilkinson power divider and branch-line coupler are composed of many quarter-wavelength transmission-line sections at a designated frequency. However, at the lower frequencies of the microwave band, the sizes of conventional Wilkinson power divider and branch-line coupler are too large for practical use. Conventionally, there are two ways to reduce the size of transmission lines. The first one is achieved by using the folded line configuration, but the resultant circuit area is still large. The other is accomplished by adopting lumped-element components, such as using the T or π equivalent model, may be employed to reduce the circuit size, however these equivalent models are useful only in a narrow bandwidth around the center frequency. In order to expand the applicable frequency range of the equivalent circuit, this thesis adopts the modified-T model for the λ/4 lines, so that the very compact designs may be implemented with no bandwidth reduction. The proposed circuit designs are accomplished by adopting balance inductors and metal-insulator-metal (MIM) capacitors so these designs may be suitable for MMIC applications. This thesis presents a compact 2.5GHz Wilkinson power divider, which is fabricated by GaAs, shows the circuit size of 0.020λg × 0.034λg, and a compact 2.5GHz branch-line coupler, which is fabricated by Glass Integrated Passive Device (GIPD), shows the circuit size of 0.021λg × 0.022λg. The circuit size is really small compared with traditional ways, and these deigns are no bandwidth reduction. In addition, a compact 2.5GHz 4 × 4 Butler matrix, which is fabricated by GIPD, is presented. The circuit size is 0.044λg × 0.047λg and the bandwidth is 34% (|S11| > 10 dB). A compact two section Wilkinson power divider is also presented in GaAs process. The circuit size is 0.044λg × 0.078λg and the bandwidth is 129.1% (|S11| > 15 dB).

碩士<br>國立中正大學<br>電機工程研究所<br>102<br>A band rejected filter with a wide tunable range for the central frequency is presented in section III. The proposed tunable filter not only provides a constant absolute bandwidth within the whole tunable frequency band, but also has a compact circuit size. The proposed tunable filter is composed of two varactor-tuned resonators, shunted at input/output ports separately, and one quarter-wavelength transmission line connecting two varactor-tuned resonators. These two varactor-tuned resonators are arranged symmetrically, and realized by a varactor and an inductor with series connection. Moreover, the varactor is introduced to control the stopband’s central frequency. The measured results show that there is a wide tunable range, 0.7 to 3 GHz, with tuning percentage of 124.3%. In addition, with insertion loss greater than 20 dB, a wide constant absolute bandwidth has been achieved at 450 MHz. Then, a simplified Butler Matrix for microwave Beam-forming System is presented in section IV. The Butler Matrix is composed of 3-dB branch-line couplers, crossovers, and phase-shift delay lines. The first input port is 180 phase difference other input ports, and the first and last output ports are added with the same degree by out of signal. This simplification can reduce input/output ports and superposition angles. By using 4  6 simplified Butler Matrix, it can realize the performance of the 8  8 Butler Matrix. As a result, this method can reduce the complexity of the circuit and total size. Measurement results show the angle change in 4  6 simplified Butler Matrix is the same as 8  8 Butler Matrix and return loss is greater than 20 dB efficiency. This design has a good isolation and the error angle is within 6.