A mathematical approach to a low power FFT architecture

Journal ArticleArchitecture and circuit design are the two most effective means of reducing power in CMOS VLSI. Mathematical manipulations have been applied to create a power efficient architecture of an FFT. This architecture has been implemented in asynchronous circuit technology that achieves significant power reduction over other FFT architectures. Multirate signal processing concepts are applied to the FFT to localize communication and remove the need for globally shared results in the FFT computation. A novel architecture is produced from the polyphase components that is mapped to an synchronous implementation. The asynchronous design continues the localization of communication and can be designed using standard cell libraries such as radiation-tolerant libraries for space electronics. We present a methodology based on multirate signal processing techniques and asynchronous design style that supports significant reduction in power over conventional design practices. A test chip implementing part of this design has been fabricated and power comparisons have been made

Multirate as a hardware paradigm

Journal ArticleArchitecture and circuit design are the two most effective means of reducing power in CMOS VLSI. Mathematical manipulations, based on applying ideas from multirate signal processing have been applied to create high performance, low power architectures. To illustrate this approach, two case studies are presented - one concerns the design of a fast Fourier transforms(FFT) device, while the other one is concerned with the design of analog-to-digital converters

From error bounds to the complexity of first-order descent methods for convex functions

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex functions having a moderately flat profile near the set of minimizers (as those of functions with H\"olderian growth). A counterexample shows that the equivalence is no longer true for extremely flat functions. This fact reveals the relevance of an approach based on KL inequality. In a second stage, we show how KL inequalities can in turn be employed to compute new complexity bounds for a wealth of descent methods for convex problems. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence in the spirit of the famous majorant method of Kantorovich. Our result applies to a very simple abstract scheme that covers a wide class of descent methods. As a byproduct of our study, we also provide new results for the globalization of KL inequalities in the convex framework. Our main results inaugurate a simple methodology: derive an error bound, compute the desingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Our method is illustrated through projection methods for feasibility problems, and through the famous iterative shrinkage thresholding algorithm (ISTA), for which we show that the complexity bound is of the form $O(q^{k})$ where the constituents of the bound only depend on error bound constants obtained for an arbitrary least squares objective with $\ell^1$ regularization

The Long-Baseline Neutrino Experiment: Exploring Fundamental Symmetries of the Universe

The preponderance of matter over antimatter in the early Universe, the dynamics of the supernova bursts that produced the heavy elements necessary for life and whether protons eventually decay --- these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our Universe, its current state and its eventual fate. The Long-Baseline Neutrino Experiment (LBNE) represents an extensively developed plan for a world-class experiment dedicated to addressing these questions. LBNE is conceived around three central components: (1) a new, high-intensity neutrino source generated from a megawatt-class proton accelerator at Fermi National Accelerator Laboratory, (2) a near neutrino detector just downstream of the source, and (3) a massive liquid argon time-projection chamber deployed as a far detector deep underground at the Sanford Underground Research Facility. This facility, located at the site of the former Homestake Mine in Lead, South Dakota, is approximately 1,300 km from the neutrino source at Fermilab -- a distance (baseline) that delivers optimal sensitivity to neutrino charge-parity symmetry violation and mass ordering effects. This ambitious yet cost-effective design incorporates scalability and flexibility and can accommodate a variety of upgrades and contributions. With its exceptional combination of experimental configuration, technical capabilities, and potential for transformative discoveries, LBNE promises to be a vital facility for the field of particle physics worldwide, providing physicists from around the globe with opportunities to collaborate in a twenty to thirty year program of exciting science. In this document we provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess.Comment: Major update of previous version. This is the reference document for LBNE science program and current status. Chapters 1, 3, and 9 provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess. 288 pages, 116 figure

Energy Resolution Performance of the CMS Electromagnetic Calorimeter

The energy resolution performance of the CMS lead tungstate crystal electromagnetic calorimeter is presented. Measurements were made with an electron beam using a fully equipped supermodule of the calorimeter barrel. Results are given both for electrons incident on the centre of crystals and for electrons distributed uniformly over the calorimeter surface. The electron energy is reconstructed in matrices of 3 times 3 or 5 times 5 crystals centred on the crystal containing the maximum energy. Corrections for variations in the shower containment are applied in the case of uniform incidence. The resolution measured is consistent with the design goals