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This work examines the problem of extending the one-dimensional analytic signal, which is ubiquitous throughout signal processing, to higher dimensional signals. Bulow et al. and Felsberg et al. have previously used techniques from Clifford algebra and analysis to extend the one-dimensional analytic signal to higher dimensions. However, each author sets forth a different definition of a multidimensional analytic signal. Herein we follow an observation of Brackx et al. and adopt a general definition of an analytic signal that encompasses both the hypercomplex signal of Bulow et al. and the monogenic signal of Felsberg et al. within the same mathematical framework. The crux of our approach is captured by the following statement: A multidimensional analytic signal is generated by an idempotent. We develop this notion more specifically using examples from geometric algebra., Comment: 27 pages, 11 figures

We use the theory of Bernstein functions, completely monotonic functions, and Levy processes to define a positive random process $\tau(t)$. For radar clutter one may think of $\tau(t)$ as the instantaneous power of the scattered radar signal that is described by a compound-Gaussian model. Thus the results herein give a mechanism for defining and simulating a compound-Gaussian random process that can be used in various radar studies. We give several examples of the sample paths of this process., Comment: 31 pages, 14 figures