EMD performance comparison: single vs double floating points

Empirical mode decomposition (EMD) is a data-driven method used to decompose data into oscillatory components. This paper examines to what extent the defined algorithm for EMD might be susceptible to data format. Two key issues with EMD are its stability and computational speed. This paper shows that for a given signal there is no significant difference between results obtained with single (binary32) and double (binary64) floating points precision. This implies that there is no benefit in increasing floating point precision when performing EMD on devices optimised for single floating point format, such as graphical processing units (GPUs)

Fast median calculation method

The ever increasing demand for high image quality requires fast and efficient methods for noise reduction. The best-known order-statistics filter is the median filter. A method is presented to calculate the median on a set of N W-bit integers in W/B time steps. Blocks containing B-bit slices are used to find B-bits of the median; using a novel quantum-like representation allowing the median to be computed in an accelerated manner compared to the best-known method (W time steps). The general method allows a variety of designs to be synthesised systematically. A further novel architecture to calculate the median for a moving set of N integers is also discussed

Running Median Algorithm and Implementation for Integer Streaming Applications

A novel algorithm is proposed to compute the median of a running window of m integers in O(lg lg m) time. For a new window, the new median value is computed as a simple decision based on the previous median and the values removed and inserted into the window. This facilitates implementations based on data structures that support fast ordinal predecessor/successor operations. The results show accelerations of up to factors of six for integer data streaming in typical embedded processors

Preprocessing 2D data for fast convex hull computations

© 2019 Cadenas, Megson. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This paper presents a method to reduce a set of n 2D points to a smaller set of s 2D points with the property that the convex hull on the smaller set is the same as the convex hull of the original bigger set. The paper shows, experimentally, that such reduction accelerates computations; the time it takes to reduce from n down to s points plus the time of computing the convex hull on the s points is less than the time to compute the convex hull on the original set of n points. The method accepts 2D points expressed as real numbers and thus extends our previous method that required points as integers. The method achieves a percentage of reduction of points of over 90% in a collections of four datasets. This amount of reduction provides speedup factors of at least two for various common convex hull algorithms. Theoretically, the reduction method executes in time within O(n) and thus is suitable for preprocessing 2D data before computing the convex hull by any known algorithm

Summary of Golden Measurements at a ν\nu-Factory

The precision and discovery potential of a neutrino factory based on muon storage rings is summarized. For three-family neutrino oscillations, we analyze how to measure or severely constraint the angle $\theta_{13}$, CP violation, MSW effects and the sign of the atmospheric mass difference $\Delta m^2_{23}$. The appearance of ``wrong-sign muons'' at three reference baselines is considered: 732 km, 3500 km and 7332 km. We exploit the dependence of the signal on the neutrino energy, and include as well realistic background estimations and detection efficiencies. The optimal baseline turns out to be $O$(3000 km).Comment: 7 pages, Latex2e, 5 eps figures, use package espfi

Golden measurements at a neutrino factory

The precision and discovery potential of a neutrino factory based on muon storage rings is studied. For three-family neutrino oscillations, we analyse how to measure or severely constraint the angle $\theta_{13}$, CP violation, MSW effects and the sign of the atmospheric mass difference $\Delta m^2_{23}$. We present a simple analytical formula for the oscillation probabilities in matter, with all neutrino mass differences non-vanishing, which clarifies the subtleties involved in disentangling the unknown parameters. The appearance of ``wrong-sign muons'' at three reference baselines is considered: 732 km, 3500 km, and 7332 km. We exploit the dependence of the signal on the neutrino energy, and include as well realistic background estimations and detection efficiencies. The optimal baseline turns out to be ${\cal O}(3000$ km). Analyses combining the information from different baselines are also presented.Comment: 45 pages, Latex2e, 24 figures using epsfig.sty. An incorrect statement and a few misprints have been corrected. Results and conclusions are unchange

C-slow retimed parallel histogram architectures for consumer imaging devices

A parallel pipelined array of cells suitable for real-time computation of histograms is proposed. The cell architecture builds on previous work obtained via C-slow retiming techniques and can be clocked at 65 percent faster frequency than previous arrays. The new arrays can be exploited for higher throughput particularly when dual data rate sampling techniques are used to operate on single streams of data from image sensors. In this way, the new cell operates on a p-bit data bus which is more convenient for interfacing to camera sensors or to microprocessors in consumer digital cameras

On the Phase Coupling of Two Components Mixing in Empirical Mode Decomposition

This paper investigates frequency mixing effect of empirical mode decomposition (EMD) and explores whether it can be explained by simple phase coupling between components of the input signal. The input is assumed to be a linear combination of harmonic oscillators. The hypothesis was tested assuming that phases of input signals’ components would couple according to Kuramoto’s model. Using a Kuramoto’s model with as many oscillators as the number of intrinsic mode functions (result of EMD), the model’s parameters were adjusted by a particle swarm optimization (PSO) method. The results show that our hypothesis is plausible, however, a different coupling mechanism than the simple sine-coupling Kuramoto’s model are likely to give better results

On the Phase Coupling of Two Components Mixing in Empirical Mode Decomposition

This paper investigates frequency mixing effect of empirical mode decomposition (EMD) and explores whether it can be explained by simple phase coupling between components of the input signal. The input is assumed to be a linear combination of harmonic oscillators. The hypothesis was tested assuming that phases of input signals’ components would couple according to Kuramoto’s model. Using a Kuramoto’s model with as many oscillators as the number of intrinsic mode functions (result of EMD), the model’s parameters were adjusted by a particle swarm optimization (PSO) method. The results show that our hypothesis is plausible, however, a different coupling mechanism than the simple sine-coupling Kuramoto’s model are likely to give better results