The Wavelet Variance , Allan Variance and Leakage
نویسندگان
چکیده
Wavelets have recently been a subject of great interest in geophysics, mathematics and signal processing. The discrete wavelet transform can be used to decompose a time series with respect to a set of basis functions, each one of which is associated with a particular scale. The properties of a time series at different scales can then be summarized by the wavelet variance, which decomposes the variance of a time series on a scale by scale basis. The wavelet variance corresponding to some of the recently discovered wavelets can provide a more accurate conversion between the time and frequency domains than can be accomplished using the Allan variance. This increase in accuracy is due to the fact that these wavelet variances give better protection against leakage than does the Allan variance.
منابع مشابه
The Allan Variance as an Estimator of the Long-memory Parameter: Time-domain and Wavelet Methods
The Allan variance is a well-known estimator of frequency stability and is often used to classify a time series into one of the standard clock noise types. By identifying the power-law model for clock noise with its long-memory equivalent, the Allan variance can also serve as an estimate for the long-memory parameter. Although the Allan variance is not a maximum likelihood estimator, it can be ...
متن کاملWavelets for the Analysis, Estimation and Synthesis of Scaling Data
Long-range dependence-Scaling phenomena-(Multi)fractal-Wavelet analysis Scaling analysis-Scaling parameters estimation-Robustness-Fractional Brownian motion synthesis-Fano factor-Aggregation procedure-Allan variance.
متن کاملLong - Memory Processes , the Allan Variance and Wavelets
Long term memory has frequently been observed in physical time series. Statistical theory for long term memory stochastic processes is radically different from the standard time series analysis, which assumes short term memory. The Allen variance is a particular measure of variability developed for long term memory processes. This variance can be interpreted as a Haar wavelet coefficient varian...
متن کاملA wavelet-based bootstrap method applied to inertial sensor stochastic error modelling using the Allan variance
A wavelet-based bootstrap method is proposed to generate surrogate data from inertial sensor noise time series and to construct bootstrap-based confidence intervals of selected parameters which are used to characterize their noise performance. The Allan variance, its links with wavelets and the whitening action of wavelet decompositions applied to long-memory stochastic processes are considered...
متن کاملAsymptotic Normality of a Hurst Parameter Estimator Based on the Modified Allan Variance
In order to estimate the memory parameter of Internet traffic data, it has been recently proposed a log-regression estimator based on the so-called modified Allan variance MAVAR . Simulations have shown that this estimator achieves higher accuracy and better confidence when compared with other methods. In this paper we present a rigorous study of the MAVAR log-regression estimator. In particula...
متن کامل