Two approximation methods to synthesize the power spectrum of fractional Gaussian noise

Abstract

The simplest models with long-range dependence (LRD) are self-similar processes. Self-similar processes have been formally considered for modeling packet traffic in communication networks. The fractional Gaussian noise (FGN) is a proper example of exactly self-similar processes. Several numeric approximation methods are considered and reviewed, two methods are found that are able to provide a better accuracy and less running time than previous approximation methods for synthesizing the power spectrum of FGN. The first method is based on a second-order approximation. It is demonstrated that a parabolic curve can be indirectly used to approximate the power spectrum of FGN. The second method is based on cubic splines. Despite the fact that splines cannot be used directly to approximate the power spectrum of FGN, they can, however, considerably simplify the calculations while maintaining high accuracy. Both of the methods proposed can be used to estimate the Hurst parameter using Whittle's estimator. Additionally, they can be used on synthesis of LRD sequences.

Hurst Parameter Estimation Using Artificial Neural Networks

“…For instance, in [16] , there is always a linear transformation that can be applied to the data so that these requirements can be easily met. For discrete-time processes, the discrete-time Fourier transform can be used [17,18,19], and the power spectral density of X is defined, for…”

“…, depends on the Hurst parameter, meaning that different values of H will produce different power spectral density functions, see [18,19]. In consequence, Equation 5 may be used to estimate H through the power spectrum components of the data series, i.e., by the amount and distribution of these components.…”

“…The main difficulty with this approach lies in accurately computing the power spectrum of FGN in a timely manner. The second-order approximation (SOA) presented in [18] estimates the power spectrum of FGN efficiently and accurately.…”

Frequency Estimation of Weighted Signals Based On DFT Interpolation Algorithm

“…For maximum side-lobe decay windows [2,3,5,7,8,13,14], w  can be written as a function of  in a simple and explicit form. For others, the polynomial approximation solution is suggested.…”

“…With the increasing application of non-linear devices and periodical time-variable loads in electrical power system, distortion of current and voltage waveforms becomes a serious problem. Therefore, a real-time analysis and control of electric power harmonic is of great significance for maintaining the electric energy quality, preventing damage to the electric network systems and saving energy [2][3]. Besides, a number of audio coding technologies have been developed recently, in which the audio signal is decomposed into sinusoids and noise before coding.…”