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The method of location and spectral estimation of weak signals on a noise background is being considered. The method is based on the optimized on order and noise dispersion autoregressive model of a sought signal. A new approach of model…
This paper studies two spectrum estimation methods for the case that the samples are obtained at a rate lower than the Nyquist rate. The first method is the correlogram method for undersampled data. The algorithm partitions the spectrum…
The problem of joint estimation of power spectrum and modulation from realizations of frequency modulated stationary wideband signals is considered. The study is motivated by some specific signal classes from which departures to…
We describe an approximate statistical model for the sample variance distribution of the non-linear matter power spectrum that can be calibrated from limited numbers of simulations. Our model retains the common assumption of a multivariate…
We derive an expression for the angular power spectrum of cosmic microwave background anisotropies due to gravity waves generated by a stochastic magnetic field and compare the result with current observations; we take into account the…
We propose a scenario that involves a stationary observer who detects a point like source of light moving with constant velocity at a constant altitude, using a telescope and a frequency-meter. We derive a formula for the angular velocity…
The angular power spectrum C_l is extracted from the 4 year COBE DMR data with a 20 degree galactic cut, using the narrowest window functions possible. The average power in eight multipole bands is also computed, and plotted together with a…
We present a general M-estimation framework for inference on the wavelet variance. This framework generalizes the results on the scale-wise properties of the standard estimator and extends them to deliver the joint asymptotic properties of…
In recent years, a rapidly growing literature has focussed on the construction of wavelet systems to analyze functions defined on the sphere. Our purpose in this paper is to generalize these constructions to situations where sections of…
Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…
We study the representations of tensor random fields on the sphere basing on the theory of representations of the rotation group. Introducing specific components of a tensor field and imposing the conditions of weak isotropy and mean square…
The energy density spectrum is an observable of gravitational waves. Divergence has appeared in the energy density spectra of the scalar induced gravitational waves for different gauge fixings. To resolve the discrepancy, we investigate the…
We establish weak convergence of the empirical process on the spherical harmonics of a Gaussian random field in the presence of an unknown angular power spectrum. This result suggests various Gaussianity tests with an asymptotic…
A method to compute several scalar quantities of Cosmic Microwave Background maps on the sphere is presented. We consider here four type of scalars: the Hessian matrix scalars, the distortion scalars, the gradient related scalars and the…
Recent measurements of the Cosmic Microwave Background Anisotropy have provided evidence for the presence of oscillations in the angular power spectrum. These oscillations are a wonderful confirmation of the standard cosmological scenario…
Several cosmological measurements have attained significant levels of maturity and accuracy over the last decade. Continuing this trend, future observations promise measurements of the statistics of the cosmic mass distribution at an…
We introduce a wavelet-based model of local stationarity. This model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time. A notion of…
Recent measurements of the cosmic microwave background radiation by the Boomerang experiment indicate that the universe is spatially flat. Here some simple back-of-the-envelope calculations are used to explain their result. The main result…
The spectral characterization of Coulomb systems confined by the homogeneous pseudo-Gaussian oscillator is investigated. This is made using the efficient computational method of generating functional. Also, the method is used for the…
Using a simple analytic model based on seed superposition we obtain the spectrum of microwave background perturbations induced by cosmic strings on all angular scales larger than about 2 armin. We assume standard recombination in an…