This place briefly explain, back supplement
Wavelet analysis of time series
Wavelet transform is localized analysis (spatial) frequency of the time, which signal (function) gradually refined by multiscale telescopic translation operation, and ultimately achieve high frequency time segment, the frequency of low frequency segments, can automatically adapt to the time-frequency requirements signal analysis, which can be focused to any details of the signal, to solve the difficult problem of Fourier transform, the Fourier transform since become a major breakthrough in the scientific method.
At time sequence studies, mainly for wavelet analysis and filtering noise canceling time series, periodic monitoring and identification information components is calculated coefficients and fractal dimension, point mutation and the analysis of multiple time scale and the like. (Dry elimination filter and I do not understand here)
It should be noted that the selection of a suitable base wavelet function is a prerequisite for wavelet analysis. In practical applications in research, should be selected for a particular situation based wavelet function required; the same time or a signal sequence, if a different group selected wavelet function, the results obtained often vary, sometimes very different. At present, mainly by comparing the error with the theoretical results obtained when different wavelet analysis signals to determine the quality of the base wavelet function, and thereby select the desired group wavelet function such studies.
The most important is to obtain wavelet coefficients by the wavelet transform equation, then these coefficients by analyzing time-series change characteristics of the frequency.
Wavelet variance with a scale change process, called wavelet variance FIG. It reflects the energy of the signal fluctuations with a scale distribution. Thus, FIG wavelet variance and used to determine the relative intensity of the main signal time scales of different kinds present scale perturbation, i.e. the primary cycle.
(This part, I painted back in the map)