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—The alternating direction multipliers method (ADMM) has been recently proposed as a practical and efficient algorithm for distributed computing. We discuss its applicability to the average consensus problem in this paper. By carefully relaxing ADMM augmentation coefficients we are able to analytically investigate its properties, and to propose simple and… (More)

—In this paper, a consensus-based clock synchronization algorithm is presented and its resilience to frequency displacement estimation errors as well as communication noise is analyzed. The synchronization-enforcing control that is to be applied to clock periods is derived upon re-casting the consensus problem into a convex optimization problem and solving… (More)

— The paper investigates the possibility for giving a general definition of the fractional Fourier transform (FRT) for all signal classes [one-dimensional (1-D) and multidimensional, continuous and discrete, periodic and aperiodic]. Since the definition is based on the eigenfunctions of the ordinary Fourier transform (FT), the preliminary conditions is that… (More)

—The multiplicity of the fractional Fourier transform (FRT), which is intrinsic in any fractional operator, has been claimed by several authors, but never systematically developed. The paper starts with a general FRT definition, based on eigen-functions and eigenvalues of the ordinary Fourier transform, which allows us to generate all possible definitions.… (More)