210 research outputs found

    Efficient algorithm for solving semi-infinite programming problems and their applications to nonuniform filter bank designs

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    An efficient algorithm for solving semi-infinite programming problems is proposed in this paper. The index set is constructed by adding only one of the most violated points in a refined set of grid points. By applying this algorithm for solving the optimum nonuniform symmetric/antisymmetric linear phase finite-impulse-response (FIR) filter bank design problems, the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorith

    An introduction to envelope constrained filter design, Journal of Telecommunications and Information Technology, 2001, nr 3

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    Envelope constrained filter design is concerned with the time domain synthesis of a filter whose response to a specified input signal stays within prescribed upper and lower bounds and in addition has minimal noise enhancement. In many practical applications, a “soft” approach, such as least mean square, is not the most suitable and it becomes necessary to use “hard” constraints such as the ones considered in the paper. We present an overview of key ideas related to robust continuous time envelope constrained filter design

    Design of Waveform Set for Multiuser Ultra-Wideband Communications

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    The thesis investigates the design of analogue waveform sets for multiuser and UWB communications using suitably chosen Hermite-Rodriguez basis functions. The non-linear non-convex optimization problem with time and frequency domains constraints has been transformed into suitable forms and then solved using a standard optimization package. The proposed approach is more flexible and efficient than existing approaches in the literature. Numerical results show that orthogonal waveform sets with high spectral efficiency can be produced

    Journal of Telecommunications and Information Technology, 2001, nr 3

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    Constrained HÌłâ‚‚ design via convex optimization with applications

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    Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1998.In title on t.p., double-underscored "H" appears in script.Includes bibliographical references (p. 133-138).A convex optimization controller design method is presented which minimizes the closed-loop H2 norm, subject to constraints on the magnitude of closed-loop transfer functions and transient responses due to specified inputs. This method uses direct parameter optimization of the closed-loop Youla or Q-parameter where the variables are the coefficients of a stable orthogonal basis. The basis is constructed using the recently rediscovered Generalized Orthonormal Basis Functions (GOBF) that have found application in system identification. It is proposed that many typical control specifications including robustness to modeling error and gain and phase margins can be posed with two simple constraints in the frequency and time domain. With some approximation, this formulation allows the controller design problem to be cast as a quadratic program. Two example applications demonstrate the practical utility of this method for real systems. First this method is applied to the roll axis of the EOS-AM1 spacecraft attitude control system, with a set of performance and robustness specifications. The constrained H2 controller simultaneously meets the specifications where previous model-based control studies failed. Then a constrained H2 controller is designed for an active vibration isolation system for a spaceborne optical technology demonstration test stand. Mixed specifications are successfully incorporated into the design and the results are verified with experimental frequency data.by Beau V. Lintereur.S.M

    Roadmap on Superoscillations

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    Superoscillations are band-limited functions with the counterintuitive property that they can vary arbitrarily faster than their fastest Fourier component, over arbitrarily long intervals. Modern studies originated in quantum theory, but there were anticipations in radar and optics. The mathematical understanding—still being explored—recognises that functions are extremely small where they superoscillate; this has implications for information theory. Applications to optical vortices, sub-wavelength microscopy and related areas of nanoscience are now moving from the theoretical and the demonstrative to the practical. This Roadmap surveys all these areas, providing background, current research, and anticipating future developments

    Zolotarev polynomials utilization in spectral analysis

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    Tato prĂĄce je zaměƙena na vybranĂ© problĂ©my ZolotarevovĂœch polynomĆŻ a jejich vyuÄŸitĂ­ ke spektrĂĄlnĂ­ analĂœze. Pokud jde o Zolotarevovy polynomy, jsou popsĂĄny zĂĄkladnĂ­ vlastnosti symetrickĂœch ZolotarevovĂœch polynomĆŻ včetně ortogonality. Rovněğ se provĂĄdĂ­ prozkoumĂĄnĂ­ numerickĂœch vlastnostĂ­ algoritmĆŻ generujĂ­cĂ­ch dokonce Zolotarevovy polynomy. Pokud jde o aplikaci ZolotarevovĂœch polynomĆŻ na spektrĂĄlnĂ­ analĂœzu, je implementovĂĄna aproximovanĂĄ diskrĂ©tnĂ­ Zolotarevova transformace, kterĂĄ umoÄŸĆˆuje vĂœpočet spektrogramu (zologramu) v reĂĄlnĂ©m čase. AproximovanĂĄ diskrĂ©tnĂ­ zolotarevskĂĄ transformace je navĂ­c upravena tak, aby lĂ©pe fungovala pƙi analĂœze tlumenĂœch exponenciĂĄlnĂ­ch signĂĄlĆŻ. A nakonec je navrÄŸena novĂĄ diskrĂ©tnĂ­ Zolotarevova transformace implementovanĂĄ plně v časovĂ© oblasti. Tato transformace takĂ© ukazuje, ÄŸe některĂ© rysy pozorovanĂ© u aproximovanĂ© diskrĂ©tnĂ­ Zolotarevovy transformace jsou dĆŻsledkem pouÄŸitĂ­ ZolotarevovĂœch polynomĆŻ.This thesis is focused on selected problems of symmetrical Zolotarev polynomials and their use in spectral analysis. Basic properties of symmetrical Zolotarev polynomials including orthogonality are described. Also, the exploration of numerical properties of algorithms generating even Zolotarev polynomials is performed. As regards to the application of Zolotarev polynomials to spectral analysis the Approximated Discrete Zolotarev Transform is implemented so that it enables computing of zologram in real–time. Moreover, the Approximated Discrete Zolotarev Transform is modified to perform better in the analysis of damped exponential signals. And finally, a novel Discrete Zolotarev Transform implemented fully in the time domain is suggested. This transform also shows that some features observed using the Approximated Discrete Zolotarev Transform are a consequence of using Zolotarev polynomials

    Bayesian Variational Regularisation for Dark Matter Reconstruction with Uncertainty Quantification

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    Despite the great wealth of cosmological knowledge accumulated since the early 20th century, the nature of dark-matter, which accounts for ~85% of the matter content of the universe, remains illusive. Unfortunately, though dark-matter is scientifically interesting, with implications for our fundamental understanding of the Universe, it cannot be directly observed. Instead, dark-matter may be inferred from e.g. the optical distortion (lensing) of distant galaxies which, at linear order, manifests as a perturbation to the apparent magnitude (convergence) and ellipticity (shearing). Ensemble observations of the shear are collected and leveraged to construct estimates of the convergence, which can directly be related to the universal dark-matter distribution. Imminent stage IV surveys are forecast to accrue an unprecedented quantity of cosmological information; a discriminative partition of which is accessible through the convergence, and is disproportionately concentrated at high angular resolutions, where the echoes of cosmological evolution under gravity are most apparent. Capitalising on advances in probability concentration theory, this thesis merges the paradigms of Bayesian inference and optimisation to develop hybrid convergence inference techniques which are scalable, statistically principled, and operate over the Euclidean plane, celestial sphere, and 3-dimensional ball. Such techniques can quantify the plausibility of inferences at one-millionth the computational overhead of competing sampling methods. These Bayesian techniques are applied to the hotly debated Abell-520 merging cluster, concluding that observational catalogues contain insufficient information to determine the existence of dark-matter self-interactions. Further, these techniques were applied to all public lensing catalogues, recovering the then largest global dark-matter mass-map. The primary methodological contributions of this thesis depend only on posterior log-concavity, paving the way towards a, potentially revolutionary, complete hybridisation with artificial intelligence techniques. These next-generation techniques are the first to operate over the full 3-dimensional ball, laying the foundations for statistically principled universal dark-matter cartography, and the cosmological insights such advances may provide

    Multiresolution image models and estimation techniques

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