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The linearization of nonlinear systems is an important digital enhancement technique. In this paper, a real-time capable post- and pre-linearization method for the widely applicable time-varying discrete-time Volterra series is presented. To this end, an alternative view on the Volterra series is established, which enables the utilization of certain modified linear iterative methods for linearization. For one particular linear iterative method, the Richardson iteration, the corresponding post- and pre-linearizers are discussed in detail. It is motivated that the resulting algorithm can be regarded as a generalization of some existing methods. Furthermore, a simply verifiable condition for convergence is presented, which allows the straightforward evaluation of applicability. The proposed method is demonstrated by means of the linearization of a time-varying nonlinear amplifier, which highlights its capability of linearizing significantly distorted signals, illustrates the advantageous convergence behavior, and depicts its robustness against modeling errors.

The factor graph approach to discrete-time linear Gaussian state space models is well developed. The paper extends this approach to continuous-time linear systems/filters that are driven by white Gaussian noise. By Gaussian message passing, we then obtain MAP/MMSE/LMMSE estimates of the input signal, or of the state, or of the output signal from noisy observations of the output signal. These estimates may be obtained with arbitrary temporal resolution. The proposed input signal estimation does not seem to have appeared in the prior Kalman filtering literature.

Acquisition is a search in two continuous dimensions, where the digital algorithms require a partitioning of the search space into cells. Depending on the partitioning of the Doppler frequency domain, more than one cell might contain significant signal energy. We present an expression for the expected values of the cells' energies to analyze the impact of the Doppler bin width on detection and false alarm probabilities., Comment: 24 pages, 12 figures; submitted

We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss convergence of various characteristics for the turbulence decay test and impacts of various components of numerical schemes on the accuracy of solutions. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the magnetic field using the constrained transport method, and using little to no explicit artificial viscosity. Codes which fall short in one or more of these areas are still useful, but they must compensate higher numerical dissipation with higher numerical resolution. This paper is the largest, most comprehensive MHD code comparison on an application-like test problem to date. We hope this work will help developers improve their numerical algorithms while helping users to make informed choices in picking optimal applications for their specific astrophysical problems., Comment: 17 pages, 5 color figures, revised version to appear in ApJ, 735, July 2011