École Polytechnique Fédérale de Lausanne
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Cloning and Characterization of lin Genes Responsible for the Degradation of Hexachlorocyclohexane Ismomers by Sphingomonas paucimobilis Strain B90
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On the Capacity of Large Gaussian Relay Networks
No full textThe capacity of a particular large Gaussian relay network is determined in the limit as the number of relays tends to infinity. Upper bounds are derived from cut-set arguments, and lower bounds follow from an argument involving uncoded transmission. It is shown that in cases of interest, upper and lower bounds coincide in the limit as the number of relays tends to infinity. Hence, this paper provides a new example where a simple cut-set upper bound is achievable, and one more example where uncoded transmission achieves optimal performance. The findings are illustrated by geometric interpretations. The techniques developed in this paper are then applied to a sensor network situation. This is a network joint source–channel coding problem, and it is well known that the source–channel separation theorem does not extend to this case. The present paper extends this insight by providing an example where separating source from channel coding does not only lead to suboptimal performance—it leads to an exponential penalty in performance scaling behavior (as a function of the number of nodes). Finally, the techniques developed in this paper are extended to include cer- tain models of ad hoc wireless networks, where a capacity scaling law can be established: When all nodes act purely as relays for a single source–destination pair, capacity grows with the logarithm of the number of nodes.LCAVLIN
Exact Sampling Results for Some Classes of Parametric Non-Bandlimited 2-D Signals
No full textWe present sampling results for certain classes of two-dimensional signals that are not bandlimited, but have a parametric representation with a finite number of degrees of freedom. While there are many such parametric signals, it is often difficult to propose practical sampling schemes, therefore, we will concentrate on those classes for which we are able to give exact sampling algorithms and reconstruction formulas. We analyze in detail a set of 2-D Diracs and extend the results to more complex objects such as lines and polygons. Unlike most multidimensional sampling schemes, the methods we propose perfectly reconstruct such signals from a finite number of samples. Some of the techniques we use are already encountered in the context of harmonic retrieval and error correction coding. In particular, singular value decomposition based methods and the annihilating filter approach are both explored as inherent parts of the proposed algorithms. Applications of our results can be found in astronomical signal processing, image processing and in some classes of identification problems.LCA
Oversampled Filter Banks
No full textPerfect reconstruction oversampled filter banks are equivalent to a particular class of frames in t(2)(Z), These frames are the subject of this paper. First, necessary and sufficient conditions on a filter bank for implementing a frame or a tight frame expansion are established, as well as a. necessary and sufficient condition for perfect reconstruction using FIR filters after an FIR analysis. Complete parameterizations of oversampled filter banks satisfying these conditions are given, Further, we study the condition under which the frame dual to the frame associated with an FIR filter bank is also FIE and give a parameterization of a class of filter banks satisfying this property, Then, we focus on nonsubsampled filter banks. Nonsubsampled filter banks implement transforms similar to continuous-time transforms and allow for very flexible design. We investigate relations of these filter banks to continuous-time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two-channel filter banks that yield highly regular wavelets with a given number of vanishing moments.LCA
Nonseparable 2-dimensional and 3-dimensional wavelets
Get PDFWe present two- and three-dimensional nonseparable wavelets. They are obtained from discrete-time bases by iterating filter banks. We consider three sampling lattices: quincunx, separable by two in two dimension, and FCO. The design methods are based either on cascade structures or on the McClellan transformation in the quincunx case. We give a few design exemples. In particular, the first example of an orthogonal 2-D wavelets basis with symetries is constructed.LCA
Orthogonal time-varying filter banks and wavelet packets
Get PDFConsiders the construction of orthogonal time-varying filter banks. By examining the time domain description of the two-channel orthogonal filter bank the authors find it possible to construct a set of orthogonal boundary filters, which allows to apply the filter bank to one-sided or finite-length signals, without redundancy or distortion. The method is constructive and complete. There is a whole space of orthogonal boundary solutions, and there is considerable freedom for optimization. This may be used to generate subband tree structures where the tree varies over time, and to change between different filter sets. The authors also show that the iteration of discrete-time time-varying filter banks gives continuous-time bases, just as in the stationary case. This gives rise to wavelet, or wavelet packet, bases for half-line and interval regionsLCA
Iterative Toeplitz solvers with local quadratic convergence
Get PDFWe study an iterative, locally quadratically convergent algorithm for solving Toeplitz systems of equations from [R. P. Brent, F. G. Gustavson and D. Y. Y. Yun. ''Fast solution of Toeplitz systems of equations and computation of Pade approximations'', J. Algorithms, 1:259-295, 1980]. We introduce a new iterative algorithm that is locally quadratically convergent when used to solve symmetric positive definite Toeplitz systems. We present a set of numerical experiments on randomly generated symmetric positive definite Toeplitz matrices. In these experiments, our algorithm performed significantly better than the previously proposed algorithm.LCA
Invertibility of linear periodically time-varying filters
Get PDFThe invertibility of linear periodically time-varying (LPTV) filters is addressed. A necessary and sufficient condition under which a LPTV filter can be inverted is shown using a LPTV postfilter. Such techniques find application, for example, in aliasing cancellation in multirate systemsLCA
Fundamental relations between the LMS algorithm and the DFT
No full textThe digital Fourier transform (DFT) and the adaptive least mean square (LMS) algorithm have existed for some time. This paper establishes a connection between them. The result is the "LMS spectrum analyzer," a new means for the calculation of the DFT. The method uses a set ofNperiodic complex phasors whose frequencies are equally spaced from dc to the sampling frequency. The phasors are weighted and then are summed to generate a reconstructed signal. Weights are adapted to realize a best least squares fit between this reconstructed signal and the input signal whose spectrum is to be estimated. The magnitude squares of the weights correspond to the power spectrum. For a proper choice of adaptation speed, the LMS spectrum analyzer will provide an exactN-sample DFT. New DFT outputs will be available in steady flow after the introduction of each new data sample.LCA