Wavelet-based detection of scaling behavior in noisy experimental data.

  title={Wavelet-based detection of scaling behavior in noisy experimental data.},
  author={Yiannis F. Contoyiannis and Stelios M. Potirakis and Fotios Diakonos},
  journal={Physical review. E},
  volume={101 5-1},
The detection of power laws in real data is a demanding task for several reasons. The two most frequently met are that (i) real data possess noise, which affects the power-law tails significantly, and (ii) there is no solid tool for discrimination between a power law, valid in a specific range of scales, and other functional forms like log-normal or stretched exponential distributions. In the present report we demonstrate, employing simulated and real data, that using wavelets it is possible to… 

Figures and Tables from this paper

Comparative Assessment of Criticality Indices Extracted from Acoustic and Electrical Signals Detected in Marble Specimens
The quantitative determination of the current load carrying capability of already loaded structural elements and the possibility to detect proper indices that could be considered as signals for
A quantum algorithm for model independent searches for new physics
We propose a novel quantum technique to search for unmodelled anomalies in multi-dimensional binned collider data. We propose to associate an Ising lattice spin site with each bin, with the Ising


A method for measuring the spectrum of a density field by the discrete wavelet transform (DWT) is studied. We show how the Fourier power spectrum can be detected by using the wavelet function
Scaling behaviour of heartbeat intervals obtained by wavelet-based time-series analysis
A new approach is introduced, based on the wavelet transform and an analytic signal approach, which can characterize non-stationary behaviour and elucidate the phase interactions between the different frequency components of the signal.
Power-Law Distributions in Empirical Data
This work proposes a principled statistical framework for discerning and quantifying power-law behavior in empirical data by combining maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov (KS) statistic and likelihood ratios.
A New Wavelet Denoising Method for Selecting Decomposition Levels and Noise Thresholds
The new method is applied to continuous wave electron spin resonance spectra and it is found that it increases the signal-to-noise ratio (SNR) by more than 32 dB without distorting the signal, whereas standard denoising methods improve the SNR by less than 10 dB and with some distortion.
Noise reduction using an undecimated discrete wavelet transform
A new nonlinear noise reduction method is presented that uses the discrete wavelet transform instead of the usual orthogonal one, resulting in a significantly improved noise reduction compared to the original wavelet based approach.
The redundant discrete wavelet transform and additive noise
  • J. Fowler
  • Computer Science
    IEEE Signal Processing Letters
  • 2005
In this letter, a precise relationship between RDWT-domain and original-signal-domain distortion for additive white noise in the RDWT domain is derived.
Processes with long-range correlations : theory and applications
Theory.- Prediction of Long-Memory Time Series: A Tutorial Review.- Fractional Brownian Motion and Fractional Gaussian Noise.- Scaling and Wavelets: An Introductory Walk.- Wavelet Estimation for the