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During the last three decades, radar wind profiling (RWP) has evolved into a key technology for atmospheric science and operational meteorology. In this tutorial status report, RWP is divided into three distinct areas: single-signal RWP, two-signal RWP, and multi-signal RWP. While single-signal RWP, or standard RWP, is a mature technology in many respects, there is still much room for improvement, particularly in the interpretation of signals that are severely contaminated by radio interference or by clutter from aircraft, birds, hydrometeors, etc. Two-signal RWP, the best known examples of which are the spaced-antenna (SA) and frequency-domain interferometry (FDI) techniques, have been used to overcome some of the limitations inherent to standard RWP. Multi-signal RWP is, to a large extent, still unexplored territory. This paper attempts to provide a coherent conceptual framework of advanced RWP and to identify areas of future research and development.

This paper is concerned with the analysis and decomposition of medical multichannel data. We present a signal processing technique that reliably detects and separates signal components such as mMCG, fMCG, or MMG by involving the spatiotemporal morphology of the data provided by the multisensor geometry of the so-called multichannel superconducting quantum interference device (SQUID) system. The mathematical building blocks are coorbit theory, multi-α-modulation frames, and the concept of joint sparsity measures. Combining the ingredients, we end up with an iterative procedure (with component-dependent projection operations) that delivers the individual signal components.

Abstract  The topic of this article is a generalization of the theory of coorbit spaces and related frame constructions to Banach spaces of functions or distributions over domains and manifolds. As a special case one obtains modulation spaces and Gabor frames on spheres. Group theoretical considerations allow first to introduce generalized wavelet transforms. These are then used to define coorbit spaces on homogeneous spaces, which consist of functions having their generalized wavelet transform in some weighted Lp space. We also describe natural ways of discretizing those wavelet transforms, or equivalently to obtain atomic decompositions and Banach frames for the corresponding coorbit spaces. Based on these facts we treat aspects of nonlinear approximation and show how the new theory can be applied to the Gabor transform on spheres. For the S1 we exhibit concrete examples of admissible Gabor atoms which are very closely related to uncertainty minimizing states. [ABSTRACT FROM AUTHOR]

This paper is concerned with generalizations and specific applications of the coorbit space theory based on group representations modulo quotients, which has been developed quite recently. We show that the general theory applied to the affine Weyl–Heisenberg group gives rise to families of smoothness spaces that can be identified with α-modulation spaces. [ABSTRACT FROM AUTHOR]

This article is concerned with frame constructions on domains and manifolds. The starting point is a unitary group representation which is square integrable modulo a suitable subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized coorbit spaces can be defined by collecting all functions for which this wavelet transform is contained in a weighted L p-space. Moreover, we show that a judicious discretization of the representation leads to an atomic decomposition and to Banach frames for these coorbit spaces. [ABSTRACT FROM AUTHOR]