A Technique to Compute Smooth Amplitude, Phase, and Frequency Modulations From the Analytic Signal

Gabor's analytic signal (AS) is a unique complex signal corresponding to a real signal, but in general, it admits infinitely-many combinations of amplitude and frequency modulations (AM and FM, respectively). The standard approach is to enforce a non-negativity constraint on the AM, but this results in discontinuities in the corresponding phase modulation (PM), and hence, an FM with discontinuities particularly when the underlying AM-FM signal is over-modulated. In this letter, we analyze the phase discontinuities and propose a technique to compute smooth AM and FM from the AS, by relaxing the non-negativity constraint on the AM. The proposed technique is effective at handling over-modulated signals. We present simulation results to support the theoretical calculations.

Perturbative expansion of the QCD Adler function improved by renormalization-group summation and analytic continuation in the Borel plane

We examine the large-order behavior of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from renormalization-group invariance. The expansion is first written as an effective series in powers of the one-loop coupling, and its leading singularities in the Borel plane are shown to be identical to those of the standard ``contour-improved'' expansion. Applying the technique of conformal mappings for the analytic continuation in the Borel plane, we define a class of improved expansions, which implement both the renormalization-group invariance and the knowledge about the large-order behavior of the series. Detailed numerical studies of specific models for the Adler function indicate that the new expansions have remarkable convergence properties up to high orders. Using these expansions for the determination of the strong coupling from the hadronic width of the tau lepton we obtain, with a conservative estimate of the uncertainty due to the nonperturbative corrections, alpha(s)(M-tau(2)) = 0.3189(-0.0151)(+0.0173), which translates to alpha(s)(M-Z(2)) = 0.1184(-0.0018)(+0.0021). DOI: 10.1103/PhysRevD.87.014008

Relook into the historical progress and philosophy of Indian space exploration

A study of the history and philosophy of the contribution of India towards the exploration of space since antiquity provides interesting insights. The contributions are described during the three periods namely: (1) the ten millenniums from 10,000 BC with a twilight period up to 900 AD; (2) the ten centuries from 900 AD to 1900 AD; and (3) the ten decades from 1900 AD to 2000 AD; called mythological, medieval, and modern respectively. Some important events during the above periods provide a reference view of the progress. The Vedas during the mythological period and the Siddhantas during the medieval periods, which are based on astronomical observations, indicate that the Indian contribution preceded other cultures. But most Western historians ignore this fact time and again in spite of many proofs provided to the contrary. This chapter also shows that Indians had the proper scientific attitude of developing any physical theory through the triplet of mind, model, and measurements. It is this same triplet that forms the basis of the present day well known Kalman filter technique. Up to about 1500 BC the Indian contribution was leading but during foreign invasion and occupation it lagged and has been improving only after independence.

On Computing Amplitude, Phase, and Frequency Modulations Using a Vector Interpretation of the Analytic Signal

The amplitude-modulation (AM) and phase-modulation (PM) of an amplitude-modulated frequency-modulated (AM-FM) signal are defined as the modulus and phase angle, respectively, of the analytic signal (AS). The FM is defined as the derivative of the PM. However, this standard definition results in a PM with jump discontinuities in cases when the AM index exceeds unity, resulting in an FM that contains impulses. We propose a new approach to define smooth AM, PM, and FM for the AS, where the PM is computed as the solution to an optimization problem based on a vector interpretation of the AS. Our approach is directly linked to the fractional Hilbert transform (FrHT) and leads to an eigenvalue problem. The resulting PM and AM are shown to be smooth, and in particular, the AM turns out to be bipolar. We show an equivalence of the eigenvalue formulation to the square of the AS, and arrive at a simple method to compute the smooth PM. Some examples on synthesized and real signals are provided to validate the theoretical calculations.

Fractional Hilbert transform extensions and associated analytic signal construction

The analytic signal (AS) was proposed by Gabor as a complex signal corresponding to a given real signal. The AS has a one-sided spectrum and gives rise to meaningful spectral averages. The Hilbert transform (HT) is a key component in Gabor's AS construction. We generalize the construction methodology by employing the fractional Hilbert transform (FrHT), without going through the standard fractional Fourier transform (FrFT) route. We discuss some properties of the fractional Hilbert operator and show how decomposition of the operator in terms of the identity and the standard Hilbert operators enables the construction of a family of analytic signals. We show that these analytic signals also satisfy Bedrosian-type properties and that their time-frequency localization properties are unaltered. We also propose a generalized-phase AS (GPAS) using a generalized-phase Hilbert transform (GPHT). We show that the GPHT shares many properties of the FrHT, in particular, selective highlighting of singularities, and a connection with Lie groups. We also investigate the duality between analyticity and causality concepts to arrive at a representation of causal signals in terms of the FrHT and GPHT. On the application front, we develop a secure multi-key single-sideband (SSB) modulation scheme and analyze its performance in noise and sensitivity to security key perturbations. (C) 2013 Elsevier B.V. All rights reserved.

The Ginibre Ensemble and Gaussian Analytic Functions

We show that as n changes, the characteristic polynomial of the n x n random matrix with i.i.d. complex Gaussian entries can be described recursively through a process analogous to Polya's urn scheme. As a result, we get a random analytic function in the limit, which is given by a mixture of Gaussian analytic functions. This suggests another reason why the zeros of Gaussian analytic functions and the Ginibre ensemble exhibit similar local repulsion, but different global behavior. Our approach gives new explicit formulas for the limiting analytic function.

Binaural Signal Processing Motivated Generalized Analytic Signal Construction and AM-FM Demodulation

Binaural hearing studies show that the auditory system uses the phase-difference information in the auditory stimuli for localization of a sound source. Motivated by this finding, we present a method for demodulation of amplitude-modulated-frequency-modulated (AM-FM) signals using a ignal and its arbitrary phase-shifted version. The demodulation is achieved using two allpass filters, whose impulse responses are related through the fractional Hilbert transform (FrHT). The allpass filters are obtained by cosine-modulation of a zero-phase flat-top prototype halfband lowpass filter. The outputs of the filters are combined to construct an analytic signal (AS) from which the AM and FM are estimated. We show that, under certain assumptions on the signal and the filter structures, the AM and FM can be obtained exactly. The AM-FM calculations are based on the quasi-eigenfunction approximation. We then extend the concept to the demodulation of multicomponent signals using uniform and non-uniform cosine-modulated filterbank (FB) structures consisting of flat bandpass filters, including the uniform cosine-modulated, equivalent rectangular bandwidth (ERB), and constant-Q filterbanks. We validate the theoretical calculations by considering application on synthesized AM-FM signals and compare the performance in presence of noise with three other multiband demodulation techniques, namely, the Teager-energy-based approach, the Gabor's AS approach, and the linear transduction filter approach. We also show demodulation results for real signals.

Multiobjective fuzzy optimization for sustainable groundwater management using particle swarm optimization and analytic element method

Groundwater management involves conflicting objectives as maximization of discharge contradicts the criteria of minimum pumping cost and minimum piping cost. In addition, available data contains uncertainties such as market fluctuations, variations in water levels of wells and variations of ground water policies. A fuzzy model is to be evolved to tackle the uncertainties, and a multiobjective optimization is to be conducted to simultaneously satisfy the contradicting objectives. Towards this end, a multiobjective fuzzy optimization model is evolved. To get at the upper and lower bounds of the individual objectives, particle Swarm optimization (PSO) is adopted. The analytic element method (AEM) is employed to obtain the operating potentio metric head. In this study, a multiobjective fuzzy optimization model considering three conflicting objectives is developed using PSO and AEM methods for obtaining a sustainable groundwater management policy. The developed model is applied to a case study, and it is demonstrated that the compromise solution satisfies all the objectives with adequate levels of satisfaction. Sensitivity analysis is carried out by varying the parameters, and it is shown that the effect of any such variation is quite significant. Copyright (c) 2015 John Wiley & Sons, Ltd.

Analytic bootstrap at large spin

We use analytic conformal bootstrap methods to determine the anomalous dimensions and OPE coefficients for large spin operators in general conformal field theories in four dimensions containing a scalar operator of conformal dimension Delta(phi). It is known that such theories will contain an in finite sequence of large spin operators with twists approaching 2 Delta(phi) + 2n for each integer n. By considering the case where such operators are separated by a twist gap from other operators at large spin, we analytically determine the n, Delta(phi) dependence of the anomalous dimensions. We find that for all n, the anomalous dimensions are negative for Delta(phi) satisfying the unitarity bound. We further compute the first subleading correction at large spin and show that it becomes universal for large twist. In the limit when n is large, we find exact agreement with the AdS/CFT prediction corresponding to the Eikonal limit of a 2-2 scattering with dominant graviton exchange.

Peierls-Nabarro model of interfacial misfit dislocation: An analytic solution

We propose a method to treat the interfacial misfit dislocation array following the original Peierls-Nabarro's ideas. A simple and exact analytic solution is derived in the extended Peierls-Nabarro's model, and this solution reflects the core structure and the energy of misfit dislocation, which depend on misfit and bond strength. We also find that only with beta < 0.2 the structure of interface can be represented by an array of singular Volterra dislocations, which conforms to those of atomic simulation. Interfacial energy and adhesive work can be estimated by inputting ab initio calculation data into the model, and this shows the method can provide a correlation between the ab initio calculations and elastic continuum theory.

Semi-analytic slope delay model for CMOS switch-level timing verification

A novel slope delay model for CMOS switch-level timing verification is presented. It differs from conventional methods in being semianalytic in character. The model assumes that all input waveforms are trapezoidal in overall shape, but that they vary in their slope. This simplification is quite reasonable and does not seriously affect precision, but it facilitates rapid solution. The model divides the stages in a switch-level circuit into two types. One corresponds to the logic gates, and the other corresponds to logic gates with pass transistors connected to their outputs. Semianalytic modeling for both cases is discussed.

Derecho natural y ciencia jurídica : consideraciones sobre la ciencia del derecho como ciencia práctica

Resumen: En el trabajo se aborda la vexata quaestio de la cientificidad de la ciencia jurídica, a la que se le impugna la pretensión de ser científica y, a la vez, práctica. Se estudian las impugnaciones realizadas en ese sentido por Claude Lévi-Strauss y Hans Albert, así como los intentos de algunos filósofos del derecho analíticos de superarla a través del análisis lógico del lenguaje jurídico. Se analizan después los cuestionamientos efectuados por algunos representantes de la filosofía hermenéutica, que critican los ensayos analíticos y proponen una concepción interpretativa de la ciencia jurídica. Luego de esta exposición, el A. evalúa las aportaciones analíticas y hermenéuticas, poniendo de relieve sus fortalezas y sus falencias a la hora de establecer el estatuto científico de la ciencia jurídica, para pasar finalmente a proponer una concepción de la ciencia del derecho heredera de la tradición de la filosofía práctica de cuño aristotélico. En este punto, el A. desarrolla —con base en el pensamiento de Tomás de Aquino— una concepción analógica del conocimiento científico y explica de qué modo es posible aplicarla a un saber acerca del derecho que resulte, a la vez, científico y práctico. Finalmente, desenvuelve la necesidad epistémica de una apertura del conocimiento de la ciencia jurídica a los primeros principios prácticos, que la vincula constitutivamente a la doctrina de la ley natural, así como al nivel máximamente determinado de la prudencia jurídica.

Part I. Hydraulics of tidal inlets: simple analytic models for the engineer

Inlets are common coastal features around the world. Essentially an inlet connects a lagoon, a bay or an estuary to the ocean (or sea), and the flow through the inlet channel is primarily induced by the tidal rise and fall of water level in the ocean. When speaking of the hydraulics of an inlet, one is interested mainly in determining the flow through the inlet and the tidal variation in the bay, given the following: (1) Inlet geometry (2) Bay geometry (3) Bottom sediment characteristics in the inlet (4) Fresh water inflow into the bay (and out through the inlet) (5) Ocean tide characteristics A combination of all these factors can produce a rather complex situation. (PDF contains 34 pages.)