We characterize the statistical properties of the frequency-wavenumber periodogram of randomly-driven waves in a hypothetical, one-dimensional, spatially inhomogeneous, stationary medium. The derived properties are used to formulate a conceptually simple test of solar oscillation power spectra to estimate the separate contributions of true dissipation and inhomogeneous structure to the linewidt...

The new health and usage monitoring systems will out perform the current ones in term of accuracy and computing time. The data therefore need to be better processed. Data in frequency domain, or spectra, are widely used thank for the richness of information. To estimate the spectrum such methods as non parametric and parametric ones may be used. This paper discusses about parametric signal spec...

This paper introduces a simple frequency domain test to discern whether two stationary time series have the same autocovariance function. The driving idea is that two stationary short-memory autocovariances coincide over all lags if and only if the corresponding spectral densities agree. As the spectral density is easily estimated via the periodogram, and the asymptotics of the periodogram are ...

Tuhin Ghosh,* Rajib Saha, Pankaj Jain, and Tarun Souradeep1,x IUCAA, Post Bag 4, Ganeshkhind, Pune-411007, India Jet Propulsion Laboratory, M/S 169-327, 4800 Oak Grove Drive, Pasadena, California 91109, USA California Institute of Technology, Pasadena, California 91125, USA Department of Physics, Indian Institute of Technology, Kanpur, U.P, 208016, India (Received 23 January 2009; published 19 ...

Second order statistics estimates in the form of sample eigenvalues and sample eigenvectors give a sub optimal description of the population density. So far only attempts have been made to reduce the bias in the sample eigenvalues. However, because the sample eigenvectors differ from the population eigenvectors as well, the population eigenvalues are biased estimates of the variances along the ...

We derive the power spectral density of timehopping (TH) spread-spectrum signals in the presence of random timing jitter, which is characterized typically by a discrete-time stationary process (independent of the TH sequences). Detailed descriptions of different TH schemes, employing a random TH sequence, is given and spectral analysis of such TH signals in the presence of uniform timing jitter...

In many practical applications second order moments are used for estimation of power spectrum. This can be cast as an inverse problem where we seek a spectrum consistent with a given state-covariance matrix. Such a solution exists if and only if the covariance matrix is positive and belong to a low dimensional subspace. The sample covariance estimate of such a matrix will typically fall outside...

6. Spectral Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Random processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Random variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Random vectors . . . . . . . . . . ....

A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function or the sample size. It puts sufficient prior mass near the true signal and automatically concentrates on its effective dimension. A rateoptimal posterior contraction is obtained in a general framework, which includes density estimation, white noise model, Gaussian sequen...