In this paper, we study the asymptotic behaviour of the angular bispectrum of spherical random fields. Here, the asymptotic theory is developed in the framework of fixed-radius fields, which are observed with increasing resolution as the sample size grows. The results we present are then exploited in a set of procedures aimed at testing non-Gaussianity; for these statistics, we are able to show...

The detection of coal/shale interfaces close to the surface using ground penetrating radar (GPR) is difficult because the echo is drowned in unwanted signal components. These components are susceptible to changes in amplitude and cannot be removed well by standard preprocessing techniques. Second order correlation based methods such as matched filtering fail to locate the echo reliably under th...

This paper presents a new noise immunity encoding/decoding technique by using the features of triple correlation and bispectrum widely employed in digital signal processing systems operating in noise environments. The triple correlationand bispectrum-based encoding/decoding algorithm is tested for a digital radio telecommunications binary frequency shift keying system. The errorless decoding pr...

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We extend the δN formalism so that it gives all of the stochastic properties of the primordial curvature perturbation ζ if the initial field perturbations are gaussian. The calculation requires only the knowledge of some family of unperturbed universes. A formula is given for the normalisation fNL of the bispectrum of ζ, which is the main signal of non-gaussianity. Examples of the use of the fo...

We provide a formula for the scaling behaviour of the inflationary bispectrum in the ‘squeezed’ limit where one momentum becomes much smaller than the other two. This determines the scaling of the halo bias at low wavenumber and will be an important observable for the next generation of galaxy surveys. Our formula allows it to be predicted for the first time for a generic inflationary model wit...

In the study of underwater signals and specially the detection of transients in a noisy background, a lot of second order methods have been developped, and a few bispectrum based techniques more recently, regarding gaussian or stationary noises. Because we are dealing with magnetic signals which are mostly diierent to the acoustic signals, we therefore use methods-in the range of Higher Order S...

Weak gravitational lensing provides a unique method to map directly the dark matter in the Universe. The majority of lensing analyses uses the two-point statistics of the cosmic shear field to constrain the cosmological model yielding degeneracies, such as that between σ8 and Ωm, respectively the r.m.s. of the mass fluctuations at a scale of 8Mpc/h and the matter density parameter both at z = 0...

The higher order spectra of order 3, ie the bispectrum and the normalised bispectrum, the bicoherence, are widely used for many engineering applications for nonlinearity and non-Gaussianity monitoring[1-9]. In particular, the bicoherence method has been applied for detection of nonlinearity and the quadratic phase coupling in waves[1], speech signals[2], control loops[3], fluids[4] and for cond...