Instantaneous frequency and amplitude of complex signals based on quaternion Fourier transform

The ideas of instantaneous amplitude and phase are well understood for signals with real-valued samples, based on the analytic signal which is a complex signal with one-sided Fourier transform. We extend these ideas to signals with complex-valued samples, using a quaternion-valued equivalent of the analytic signal obtained from a one-sided quaternion Fourier transform which we refer to as the hypercomplex representation of the complex signal. We present the necessary properties of the quaternion Fourier transform, particularly its symmetries in the frequency domain and formulae for convolution and the quaternion Fourier transform of the Hilbert transform. The hypercomplex representation may be interpreted as an ordered pair of complex signals or as a quaternion signal. We discuss its derivation and properties and show that its quaternion Fourier transform is one-sided. It is shown how to derive from the hypercomplex representation a complex envelope and a phase. A classical result in the case of real signals is that an amplitude modulated signal may be analysed into its envelope and carrier using the analytic signal provided that the modulating signal has frequency content not overlapping with that of the carrier. We show that this idea extends to the complex case, provided that the complex signal modulates an orthonormal complex exponential. Orthonormal complex modulation can be represented mathematically by a polar representation of quaternions previously derived by the authors. As in the classical case, there is a restriction of non-overlapping frequency content between the modulating complex signal and the orthonormal complex exponential. We show that, under these conditions, modulation in the time domain is equivalent to a frequency shift in the quaternion Fourier domain. Examples are presented to demonstrate these concepts

LongITools:Dynamic longitudinal exposome trajectories in cardiovascular and metabolic noncommunicable diseases

The current epidemics of cardiovascular and metabolic noncommunicable diseases have emerged alongside dramatic modifications in lifestyle and living environments. These correspond to changes in our "modern" postwar societies globally characterized by rural-to-urban migration, modernization of agricultural practices, and transportation, climate change, and aging. Evidence suggests that these changes are related to each other, although the social and biological mechanisms as well as their interactions have yet to be uncovered. LongITools, as one of the 9 projects included in the European Human Exposome Network, will tackle this environmental health equation linking multidimensional environmental exposures to the occurrence of cardiovascular and metabolic noncommunicable diseases

Figurative language processing in atypical populations: the ASD perspective

This document is protected by copyright and was first published by Frontiers. All rights reserved. It is reproduced with permissionThis paper is intended to provide a critical overview of experimental and clinical research documenting problems in figurative language processing in atypical populations with a focus on the Autistic Spectrum. Research in the comprehension and processing of figurative language in autism invariably documents problems in this area. The greater paradox is that even at the higher end of the spectrum or in the cases of linguistically talented individuals with Asperger syndrome, where structural language competence is intact, problems with extended language persist. If we assume that figurative and extended uses of language essentially depend on the perception and processing of more concrete core concepts and phenomena, the commonly observed failure in atypical populations to understand figurative language remains a puzzle. Various accounts have been offered to explain this issue, ranging from linking potential failure directly to overall structural language competence (Norbury, 2005; Brock et al., 2008) to right-hemispheric involvement (Gold and Faust, 2010). We argue that the dissociation between structural language and figurative language competence in autism should be sought in more general cognitive mechanisms and traits in the autistic phenotype (e.g., in terms of weak central coherence, Vulchanova et al., 2012b), as well as failure at on-line semantic integration with increased complexity and diversity of the stimuli (Coulson and Van Petten, 2002). This perspective is even more compelling in light of similar problems in a number of conditions, including both acquired (e.g., Aphasia) and developmental disorders (Williams Syndrome). This dissociation argues against a simple continuity view of language interpretation

LongITools: Dynamic longitudinal exposome trajectories in cardiovascular and metabolic noncommunicable diseases

The current epidemics of cardiovascular and metabolic noncommunicable diseases have emerged alongside dramatic modifications in lifestyle and living environments. These correspond to changes in our “modern” postwar societies globally characterized by rural-to-urban migration, modernization of agricultural practices, and transportation, climate change, and aging. Evidence suggests that these changes are related to each other, although the social and biological mechanisms as well as their interactions have yet to be uncovered. LongITools, as one of the 9 projects included in the European Human Exposome Network, will tackle this environmental health equation linking multidimensional environmental exposures to the occurrence of cardiovascular and metabolic noncommunicable diseases

LongITools: Dynamic longitudinal exposome trajectories in cardiovascular and metabolic noncommunicable diseases

The current epidemics of cardiovascular and metabolic noncommunicable diseases have emerged alongside dramatic modifications in lifestyle and living environments. These correspond to changes in our “modern” postwar societies globally characterized by rural-to-urban migration, modernization of agricultural practices, and transportation, climate change, and aging. Evidence suggests that these changes are related to each other, although the social and biological mechanisms as well as their interactions have yet to be uncovered. LongITools, as one of the 9 projects included in the European Human Exposome Network, will tackle this environmental health equation linking multidimensional environmental exposures to the occurrence of cardiovascular and metabolic noncommunicable diseases.</p