The moving chest wall imparts a delay modulation onto the reflected IR-UWB radar signal, making the radar return a nonlinear function of chest wall displacement. Existing theoretical spectral models of the IR-UWB radar reflections from the human chest wall have restrictive assumptions that preclude realistic modeling of chest wall displacement and assume an aliased version of the radar signal. This paper presents novel theoretical analysis of the un-aliased spectrum, without the restrictive assumptions. Potential applications not specifically treated in this paper, but illustrative of the novelty and broader scope of the presented analysis, include heart-induced displacements that are realistically more bursty in nature and breathing-induced displacements consistent with, for example, non-unity inspiration-to-expiration ratios characteristic of asthma; neither of these could be analyzed using previous models. As well known, the un-aliased spectrum cannot generally be recovered from the aliased spectrum. In particular, the paper shows that the clusters of the non-aliased spectrum are not just scaled versions of each other; rather they have complex variations that if measurable, could enable estimation of parameters such as displacement amplitude; such variations are not apparent in the existing aliased spectrum model, which has just one cluster. This paper analyzes the degree to which the aliased model di↵ers from the non-aliased model. The paper also addresses some practical aspects of the spectral model, such as the number of significant components in a spectral cluster and computational complexity of the theoretical model.
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