Oversampling in shift-invariant spaces with a rational sampling period

8 pages, no figures.It is well known that, under appropriate hypotheses, a sampling formula allows us to recover any function in a principal shift-invariant space from its samples taken with sampling period one. Whenever the generator of the shift-invariant space satisfies the Strang-Fix conditions of order r, this formula also provides an approximation scheme of order r valid for smooth functions. In this paper we obtain sampling formulas sharing the same features by using a rational sampling period less than one. With the use of this oversampling technique, there is not one but an infinite number of sampling formulas. Whenever the generator has compact support, among these formulas it is possible to find one whose associated reconstruction functions have also compact support.This work has been supported by the Grant MTM2009-08345 from the D.G.I. of the Spanish Ministerio de Ciencia y Tecnología

Riesz bases in L2(0,1) related to sampling in shift-invariant spaces

AbstractThe Fourier duality is an elegant technique to obtain sampling formulas in Paley–Wiener spaces. In this paper it is proved that there exists an analogue of the Fourier duality technique in the setting of shift-invariant spaces. In fact, any shift-invariant space Vφ with a stable generator φ is the range space of a bounded one-to-one linear operator T between L2(0,1) and L2(R). Thus, regular and irregular sampling formulas in Vφ are obtained by transforming, via T, expansions in L2(0,1) with respect to some appropriate Riesz bases

Sampling in unitary invariant subspaces associated to LCA groups

In this paper a sampling theory for unitary invariant subspaces associated to locally compact abelian (LCA) groups is deduced. Working in the LCA group context allows to obtain, in a unified way, sampling results valid for a wide range of problems which are interesting in practice, avoiding also cumbersome notation. Along with LCA groups theory, the involved mathematical technique is that of frame theory which meets matrix analysis when appropriate dual frames are computed

Regular generalized sampling in T-invariant subspaces of a Hilbert space

A regular generalized sampling theory in some structured T-invariant subspaces of a Hilbert space H, where T denotes a bounded invertible operator in H, is established in this paper. This is done by walking through the most important cases which generalize the usual sampling settings.Comment: 23 page

A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling

The aim of this work is to solve a question raised for average sampling in shift-invariant spaces by using the well-known matrix pencil theory. In many common situations in sampling theory, the available data are samples of some convolution operator acting on the function itself: this leads to the problem of average sampling, also known as generalized sampling. In this paper we deal with the existence of a sampling formula involving these samples and having reconstruction functions with compact support. Thus, low computational complexity is involved and truncation errors are avoided. In practice, it is accomplished by means of a FIR filter bank. An answer is given in the light of the generalized sampling theory by using the oversampling technique: more samples than strictly necessary are used. The original problem reduces to finding a polynomial left inverse of a polynomial matrix intimately related to the sampling problem which, for a suitable choice of the sampling period, becomes a matrix pencil. This matrix pencil approach allows us to obtain a practical method for computing the compactly supported reconstruction functions for the important case where the oversampling rate is minimum. Moreover, the optimality of the obtained solution is established

Current and prospective pharmacological targets in relation to antimigraine action

Migraine is a recurrent incapacitating neurovascular disorder characterized by unilateral and throbbing headaches associated with photophobia, phonophobia, nausea, and vomiting. Current specific drugs used in the acute treatment of migraine interact with vascular receptors, a fact that has raised concerns about their cardiovascular safety. In the past, α-adrenoceptor agonists (ergotamine, dihydroergotamine, isometheptene) were used. The last two decades have witnessed the advent of 5-HT1B/1D receptor agonists (sumatriptan and second-generation triptans), which have a well-established efficacy in the acute treatment of migraine. Moreover, current prophylactic treatments of migraine include 5-HT2 receptor antagonists, Ca2+ channel blockers, and β-adrenoceptor antagonists. Despite the progress in migraine research and in view of its complex etiology, this disease still remains underdiagnosed, and available therapies are underused. In this review, we have discussed pharmacological targets in migraine, with special emphasis on compounds acting on 5-HT (5-HT1-7), adrenergic (α1, α2, and β), calcitonin gene-related peptide (CGRP 1 and CGRP2), adenosine (A1, A2, and A3), glutamate (NMDA, AMPA, kainate, and metabotropic), dopamine, endothelin, and female hormone (estrogen and progesterone) receptors. In addition, we have considered some other targets, including gamma-aminobutyric acid, angiotensin, bradykinin, histamine, and ionotropic receptors, in relation to antimigraine therapy. Finally, the cardiovascular safety of current and prospective antimigraine therapies is touched upon

Atlas de las praderas marinas de España

Knowledge of the distribution and extent of seagrass habitats is currently the basis of management and conservation policies of the coastal zones in most European countries. This basic information is being requested through European directives for the establishment of monitoring programmes and the implementation of specific actions to preserve the marine environment. In addition, this information is crucial for the quantification of the ecological importance usually attributed to seagrass habitats due to, for instance, their involvement in biogeochemical cycles, marine biodiversity and quality of coastal waters or global carbon budgets. The seagrass atlas of Spain represents a huge collective effort performed by 84 authors across 30 Spanish institutions largely involved in the scientific research, management and conservation of seagrass habitats during the last three decades. They have contributed to the availability of the most precise and realistic seagrass maps for each region of the Spanish coast which have been integrated in a GIS to obtain the distribution and area of each seagrass species. Most of this information has independently originated at a regional level by regional governments, universities and public research organisations, which explain the elevated heterogeneity in criteria, scales, methods and objectives of the available information. On this basis, seagrass habitats in Spain occupy a total surface of 1,541,63 km2, 89% of which is concentrated in the Mediterranean regions; the rest is present in sheltered estuarine areas of the Atlantic peninsular regions and in the open coastal waters of the Canary Islands, which represents 50% of the Atlantic meadows. Of this surface, 71.5% corresponds to Posidonia oceanica, 19.5% to Cymodocea nodosa, 3.1% to Zostera noltii (=Nanozostera noltii), 0.3% to Zostera marina and 1.2% to Halophila decipiens. Species distribution maps are presented (including Ruppia spp.), together with maps of the main impacts and pressures that has affected or threatened their conservation status, as well as the management tools established for their protection and conservation. Despite this considerable effort, and the fact that Spain has mapped wide shelf areas, the information available is still incomplete and with weak precision in many regions, which will require an investment of major effort in the near future to complete the whole picture and respond to demands of EU directives

Atlas de las praderas marinas de España

Knowledge of the distribution and extent of seagrass habitats is currently the basis of management and conservation policies of the coastal zones in most European countries. This basic information is being requested through European directives for the establishment of monitoring programmes and the implementation of specific actions to preserve the marine environment. In addition, this information is crucial for the quantification of the ecological importance usually attributed to seagrass habitats due to, for instance, their involvement in biogeochemical cycles, marine biodiversity and quality of coastal waters or global carbon budgets. The seagrass atlas of Spain represents a huge collective effort performed by 84 authors across 30 Spanish institutions largely involved in the scientific research, management and conservation of seagrass habitats during the last three decades. They have contributed to the availability of the most precise and realistic seagrass maps for each region of the Spanish coast which have been integrated in a GIS to obtain the distribution and area of each seagrass species. Most of this information has independently originated at a regional level by regional governments, universities and public research organisations, which explain the elevated heterogeneity in criteria, scales, methods and objectives of the available information. On this basis, seagrass habitats in Spain occupy a total surface of 1,541,63 km2, 89% of which is concentrated in the Mediterranean regions; the rest is present in sheltered estuarine areas of the Atlantic peninsular regions and in the open coastal waters of the Canary Islands, which represents 50% of the Atlantic meadows. Of this surface, 71.5% corresponds to Posidonia oceanica, 19.5% to Cymodocea nodosa, 3.1% to Zostera noltii (=Nanozostera noltii), 0.3% to Zostera marina and 1.2% to Halophila decipiens. Species distribution maps are presented (including Ruppia spp.), together with maps of the main impacts and pressures that has affected or threatened their conservation status, as well as the management tools established for their protection and conservation. Despite this considerable effort, and the fact that Spain has mapped wide shelf areas, the information available is still incomplete and with weak precision in many regions, which will require an investment of major effort in the near future to complete the whole picture and respond to demands of EU directives.Versión del edito