The behaviour of averaged periodograms and cross-periodograms of a broad class of nonstationary processes is studied. The processes include nonstationary ones that are fractional of any order, as well as asymptotically stationary fractional ones, and the cross-periodogram can involve two nonstationary processes of possibly different orders, or a nonstationary and an asymptotically stationary on...

This paper demonstrates and exploits some interesting frequency-domain properties of nonstationary signals. Considering these properties, a new method for blind separation of linear instantaneous mixtures of mutually uncorrelated, nonstationary, real sources is proposed which is based on spectral decorrelation of the sources. It allows the existing timedomain algorithms developed for stationary...

In this paper we shall characterize Sobolev spaces of an arbitrary order of smoothness using nonstationary tight wavelet frames for L2(R). In particular, we show that a Sobolev space of an arbitrary fixed order of smoothness can be characterized in terms of the weighted `2-norm of the analysis wavelet coefficient sequences using a fixed compactly supported nonstationary tight wavelet frame in L...

For nonstationary time series consisting ofmultiple time-varying frequency (TVF) componentswhere the frequency of components overlaps in time, classical linear filters fail to extract components. The G-filter based on time deformation has been developed to extract components of multicomponent G-stationary processes. In this paper, we explore the wide application of the G-filter for filtering di...

Abstract Assume that observations are generated from a nonstationary autoregressive (AR) processes of infinite order. We adopt a finite-order approximation model to predict future observations and obtain an asymptotic expression for the mean-squared prediction error (MSPE) of the least squares predictor. This expression provides the first exact assessment of the impacts of nonstationarity, mode...