Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

http://ahvazdownload.persiangig.com/document/article/39.pdf

A wavelet tour of signal processing

https://www.tau.ac.il/%7Eklafter1/258.pdf

The random walk's guide to anomalous diffusion: a fractional dynamics approach

Demonstrates that Ethernet LAN traffic is statistically self-similar, that none of the commonly used traffic models is able to capture this fractal-like behavior, that such behavior has serious implications for the design, control, and analysis of high-speed, cell-based networks, and that aggregating streams of such traffic typically intensifies the self-similarity ("burstiness") instead of smoothing it. These conclusions are supported by a rigorous statistical analysis of hundreds of millions of high quality Ethernet traffic measurements collected between 1989 and 1992, coupled with a discussion of the underlying mathematical and statistical properties of self-similarity and their relationship with actual network behavior. The authors also present traffic models based on self-similar stochastic processes that provide simple, accurate, and realistic descriptions of traffic scenarios expected during B-ISDN deployment. >

/pdf/on-the-self-similar-nature-of-ethernet-traffic-extended-3i4efiwsq9.pdf

On the self-similar nature of Ethernet traffic (extended version)

. The idea of fractional differencing is introduced in terms of the infinite filter that corresponds to the expansion of (1-B)d. When the filter is applied to white noise, a class of time series is generated with distinctive properties, particularly in the very low frequencies and provides potentially useful long-memory forecasting properties. Such models are shown to possibly arise from aggregation of independent components. Generation and estimation of these models are considered and applications on generated and real data presented.

An introduction to long‐memory time series models and fractional differencing

. The definitions of fractional Gaussian noise and integrated (or fractionally differenced) series are generalized, and it is shown that the two concepts are equivalent. A new estimator of the long memory parameter in these models is proposed, based on the simple linear regression of the log periodogram on a deterministic regressor. The estimator is the ordinary least squares estimator of the slope parameter in this regression, formed using only the lowest frequency ordinates of the log periodogram. Its asymptotic distribution is derived, from which it is evident that the conventional interpretation of these least squares statistics is justified in large samples. Using synthetic data the asymptotic theory proves to be reliable in samples of 50 observations or more. For three postwar monthly economic time series, the estimated integrated series model provides more reliable out-of-sample forecasts than do more conventional procedures.

The estimation and application of long memory time series models

Fractional Brownian Motions, Fractional Noises and Applications

: A family of Gaussian processes, called fractional Brownian motion, which arise naturally from an examination of the conditions of validity of the central limit theorem, is studied. Fractional Brownian motion possesses an important property of 'self-similarity.' This property leads to a more general class of processes, not necessarily Gaussian, called self-similar processes. This paper is addressed to mathematicians, scientists, and engineers; the material is arranged in order of increasing mathematical sophistication. (Author)

John W. Van Ness

Papers

Fractional Brownian Motions, Fractional Noises and Applications

Fractional brownian motion, self-similar processes, and applications,

Probability (John Lamperti)