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, 24, 395–457.References: results as anotherand one function will give the same qualitativethen the choice of wavelet function is not critical,is primarily interested in wavelet power spectra,smooth function such as a damped cosine. If onesmoothly varying time series one would choose aa boxcar-like function such as the Harr, while forwith sharp jumps or steps, one would chooseof features present in the time series. For time series4) Shape. The wavelet function should reflect the typegood frequency resolution.broad function will have poor time resolution, yetresolution but poor frequency resolution, while aA narrow (in time) function will have good timewidth in real space and the width in Fourier space.
function is determined by the balance between thewavelet amplitude. The resolution of a waveletfunction is defined here as the e-folding time of the3) Width. For concreteness, the width of a waveletor discontinuities.single component and can be used to isolate peaksA real wavelet function returns only aand is better adapted for capturing oscillatory behavior.return information about both amplitude and phase2) Complex or real. A complex wavelet function willamplitude are expected.where smooth, continuous variations in wavelettransform is useful for time series analysis,times is highly correlated. The nonorthogonalat large scales, where the wavelet spectrum at adjacent(such as used in this study) is highly redundantspectrum.
Conversely, a nonorthogonal analysisshift in the time series produces a different waveletfor time series analysis, an aperiodicthe most compact representation of the signal. Unfortunatelypower and is useful for signal processing as it givesthat contains discrete “blocks” of waveletbasis at that scale. This produces a wavelet spectrumeach scale is proportional to the width of the waveletwavelet analysis, the number of convolutions at1) Orthogonal or nonorthogonal. In orthogonal Bessel, Legendre, etc.
) In choosing the wavelet function, there are several factors which should be considered (for more discussion see Farge 1992).One criticism of wavelet analysis is the arbitrary choice of the wavelet function, y0(h). (It should be noted that the same arbitrary choice is made in using one of the more traditional transforms such as the Fourier,Functions of Wavelet transform of such capability is not given.in frequency. The conventional two dimensional Fourieraccuracy simultaneously both in a time-domain, andallows to conduct the analysis with the necessaryaxis – shift state, another – parameter of scaling.
Itresearched signal appears to be two dimensional: oneand called as wavelet. The wavelet-spectrum of abasis only one functions possessing special propertiesthe help of stretching-compressions and shifts on thearea. This basis is remarkable because it is built withrestricted both in temporary, and in frequencydecomposition of a parsed signal on basis of functions,century 2,3. The essence of the method consists inmethod was designed in middle 80s of the twentiethThe wavelet analysis as a new mathematicalwavelet analysis is represented.
techniques of such signals. Expedient usage of theis the application of new mathematical researchOne of possible paths of escaping of the given situationWavelet Analysis Wavelet analysis is becoming a common tool for analyzing localized variations of power within a time series. By decomposing a time series into time–frequency space, one is able to determine both the dominant modes of variability and how those modes vary in time. at infinity does not play any role.analyzing wavelet before convolving it with the signal. The limited spatial support of wavelets is important because then the behavior of the signaluse analyzing functions, called wavelets, which are localized in space.1 The scale decomposition is obtained by dilating or contracting the chosenWavelets are mathematical techniques, based on group theory and square integrable representations, which allows one to unfold a signal, or a field, into both space and scale, and possibly directions.
They number of techniques which had been developed independently for various signal processing applications.Wavelet theory based on unified framework for a Introduction: