Many time series in the applied sciences display a time-varying second order structure. In this article, we address the problem of how to forecast these non-stationary time series by means of non-decimated wavelets. We first consider a model in which only the variance evolves with time. We define a predictor for this model and show an application to the Dow Jones index. Then, we generalise the ...

Abstract: A new finite impulse response (FIR) prediction is presented for a state space signal model. The linear predictor proposed in this paper uses the finite number of inputs and outputs on the recent time interval while the infinite impulse response (IIR) predictor with feedback and recursion uses all inputs and outputs from the initial time to the current time. The Yule-Walker equations f...

Non-parametric methods of Spectrum Estimation Such as Periodogram, Modified Periodogram, Welch, Bartlett and Blackman-Tukey are generally used but are not always efficient in finding out the power spectral densities. These methods lacks due to their limitations like windowing of the autocorrelation sequence, spectral leakage, poor resolution and incapability to include the available information...

We consider the analysis of time series data, with particular emphasis on series which have a heavy-tailed structure | that is, whose marginal distributions have a right tail which is regularly varying at innnity with index ?. A natural model to attempt to t to time series data is an autoregression of order p, where p itself is often determined from the data. Recently several methods of paramet...

Recent progress in signal processing and estimation has generated considerable interest in the problem of computing the smallest eigenvalue of symmetric positive definite Toeplitz matrices. Several algorithms have been proposed in the literature. Many of them compute the smallest eigenvalue in an iterative fashion, relying on the Levinson–Durbin solution of sequences of Yule–Walker systems. Exp...

Acoustic impulse responses of an excavated tunnel were measured. Analysis of the impulse responses shows that they are very diffuse from the start. A reverberator suitable for reproducing this type of response is proposed. The input signal is first comb-filtered and then convolved with a sparse noise sequence of the same length as the filter’s delay line. An IIR loop filter inside the comb filt...

A ∆Σ modulator that is often utilized to convert analog signals into digital signals can be modeled as a static uniform quantizer with an error feedback filter. In this paper, we present a rate-distortion analysis of quantizers with error feedback including the ∆Σ modulators, assuming that the error owing to overloading in the static quantizer is negligible. We demonstrate that the amplitude re...

Abstract. In this paper we will present a general framework for solving linear systems of equations. The solver is based on the Levinson-idea for solving Toeplitz systems of equations. We will consider a general class of matrices, defined as the class of simple -Levinson conform matrices. This class incorporates, for instance, semiseparable, band, companion, arrowhead and many other matrices. F...