Analyzing subtle features of natural time series by means of a wavelet-based approach

Abstract

The present paper is devoted to the development of methods and approaches intended for the analysis of natural time series. Due to the strong variability, irregularity, and complex structure of the time series in question, the problem of automatic processing, i.e., in automatic mode, is rather complicated and merits further investigation in order to produce better solutions than those that presently exist. Relying on contemporary methods of signal processing, signal analysis, and recognition of complex data, we have suggested a new wavelet based approach, which allows one to extract subtle structural features from a complex natural time series in an automatic mode. After that, it becomes possible to identify these features and analyze them in terms of a particular knowledge domain. Our methods and approaches have been successfully tested on the Earth's magnetic field data obtained from the Paratunka observatory (Paratunka village, Kamchatka region, Far East of Russia).

Ionospheric parameter modelling and anomaly discovery by combining the wavelet transform with autoregressive models

“…Using multiresolution decompositions to level m we can represent the original data the following way [Mandrikova et al 2011[Mandrikova et al , 2012c[Mandrikova et al , 2013a:…”

“…Wavelet-based approaches have been broadly applied to multiple areas of signal processing and related fields in the last twenty years [Al-Kasasbeh 2004, Mandrikova and Bogdanov 2007, Li et al 2009, Vargas-Bracamontes et al 2009, Beltrán and Ponce de León 2010, Hafez et al 2010, Mandrikova et al 2010, Hafez and Ghamry 2011, Liming et al 2011, Mandrikova et al 2011, Wang et al 2011, Gwal et al 2012, Mandrikova et al 2012b, Mandrikova et al 2012c, Bakhshi et al 2013, Castillo et al 2013, Han and Chang 2013, Mandrikova et al 2013a]. These methods encompass some elements of the approximation theory [Donoho andJohnstone 1998, Mallat 1999] and filtering [Mitra 1998] and in many cases they help us to solve the tasks in question [Vargas-Bracamontes et al 2009, Mandrikova et al 2012a, Mandrikova et al 2012b, Mandrikova et al 2012c, Mandrikova et al 2013a]. Owing to a wide range of existing wavelet bases with compact support, wavelets provide special opportunities for detailed studies of complex data structure.…”

A Novel Recognition Algorithm Based on Optimal Wavelet Packet and Non-Negative Matrix Factorization for Extracting Pathologic Features of Plant Image

“…If the function family {wn(t)}n∈Z is set as wavelet packet [11] generated by the scaling function W0(t)= ) (t φ of the orthonormal wavelet basis, then they have the translation orthogonality, i.e.…”

Study of nonlinear time series and wavelet power spectrum analysis using solar wind parameters and geomagnetic indices

“…Also, wavelet power spectrum (WPS) have been widely used in numerous-related fields (Beltrán and Ponce de León 2010;Hafez et al 2010;Mandrikova et al 2010Mandrikova et al , 2011Mandrikova et al , 2012aMandrikova et al , 2012bMandrikova et al , 2012cMandrikova et al , 2013Hafez and Ghamry 2011;Liming et al 2011;Ghamry et al 2012;Gwal et al 2012;Bakhshi et al 2013;Castillo et al 2013;Han and Chang 2013). WPS present facts on the amplitude of phase signals during the time series and how its amplitude changes with time.…”