Tomaso Erseghe

Unified fractional Fourier transform and sampling theorem

The fractional Fourier transform (FRT) is an extension of the ordinary Fourier transform (FT). Applying the language of the unified FT, we develop FRT expressions for discrete and continuous signals, introducing a particular form of periodicity: chirp-periodicity. The FRT sampling theorem is derived as an extension of its ordinary counterpart.

Distributed Optimal Power Flow Using ADMM

Distributed optimal power flow (OPF) is a challenging non-linear, non-convex problem of central importance to the future power grid. Although many approaches are currently available in the literature, these require some form of central coordination to properly work. In this paper a fully distributed and robust algorithm for OPF is proposed which does not require any form of central coordination. The algorithm is based upon the alternating direction multiplier method (ADMM) in a form recently proposed by the author, which, in turn, builds upon the work of Schizas The approach is customized as a region-based optimization procedure, and it is tested in meaningful scenarios.

Fast Consensus by the Alternating Direction Multipliers Method

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 strict analytical bounds. These provide a clear indication on how to choose system parameters for optimized performance. We prove both analytically and via simulations that the proposed approach exhibits convergence speed between the best in the literature (classical and optimized solutions), while providing the most powerful resilience to noise.

Multiplicity of fractional Fourier transforms and their relationships

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 eigenfunctions and eigenvalues of the ordinary Fourier transform, which allows us to generate all possible definitions. The multiplicity is due to different choices of both the eigenfunction and the eigenvalue classes. A main result, obtained by a generalized form of the sampling theorem, gives explicit relationships between the different FRTs.

A unified framework for the fractional Fourier transform

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 the signal domain/periodicity be the same as the FT domain/periodicity. Within these classes, a general FRT definition is formulated, and the FRT properties are established. In addition, the multiplicity (which is intrinsic in a fractional operator) is clearly developed. The general definition is checked in the case in which the FRT is presently available and, moreover, to establish the FRT in new classes of signals.

The fractional discrete cosine transform

The extension of the Fourier transform operator to a fractional power has received much attention in signal theory and is finding attractive applications. The paper introduces and develops the fractional discrete cosine transform (DCT) on the same lines, discussing multiplicity and computational aspects. Similarities and differences with respect to the fractional Fourier transform are pointed out.

A multicarrier architecture based upon the affine Fourier transform

Recently, innovative multicarrier schemes have been proposed that exploit the transmission of chirp-shaped waves e/sup -j2/spl pi/ct2/ by optimally choosing the chirp parameter c on the basis of the channel characteristics and are more robust to time-varying channels than ordinary OFDM schemes. This concept was applied to continuous-time and to discrete-time systems. In the present paper, we aim at developing those ideas using the affine Fourier transform (AFT), which is a very general formulation of chirp transforms. We present a multicarrier modulation based upon the discrete form of the AFT that is therefore inherently discrete and strictly invertible. Moreover, it allows to define a circular prefix concept that is coherent with the chirp nature of the transmission. The system can be efficiently implemented by adding a simple phase-correction block to standard OFDM modulators/demodulators and can effectively combat interchannel interference when the propagation channel is made of few multipath components affected by independent frequency offsets. Our discrete-time multicarrier scheme is an improved version of Martones approach (as we also show by simulation results), and exhibits analogous characteristics to Barbarossas continuous-time system.

On UWB Impulse Radio Receivers Derived by Modeling MAI as a Gaussian Mixture Process

One of the main problems in ultra wide band (UWB) impulse radio (IR) systems is the need to cope efficiently with multiple access interference (MAI). As outlined recently in the literature, this can be achieved by modeling MAI as a Gaussian mixture (GM) random process and deriving the receiver in accordance with a maximum likelihood paradigm. Depending on the chosen context, both rake and chip-matched solutions can be identified. In this paper we compare different solutions, generalize them to a QAM context, and investigate their implementation complexity and robustness to impulsive interference. We also investigate efficient methods to lower the computational demand.

Power Flow Optimization for Smart Microgrids by SDP Relaxation on Linear Networks

In a smart microgrid currents injected by distributed energy resources (DERs) and by the point of common coupling can be adapted to minimize the energy cost. Design and quality constraints usually make the problem grow fast with the number of nodes in the network. In this paper we provide a solution to the optimization problem having a significantly reduced complexity with respect to existing techniques. The efficiency of the proposed solution stems by modeling the smart microgrid as a linear network where loads are approximated as impedances. This simplification allows avoiding explicit use of power flow equations, and having a number of equation proportional to the number of DERs rather than to the total number of nodes (loads and DERs). The optimal power flow problem is then solved by a semidefinite programming (SDP) relaxation, which provides the initial point for the search of a feasible solution by a sequential convex programming procedure based on a local linear approximation of non-convex constraints. Numerical results show the merits of the proposed approach for typical smart microgrid scenarios.

Method for defining a class of fractional operations

The fractional Fourier transform (FRT) permits a variety of associated fractional operations. This correspondence proposes a systematic method, based on the structure of the FRT, which not only provides unambiguous extensions of ordinary operations but permits writing the applicable expressions simply by inspection. The approach also exposes the possible paths for implementing such operations.