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The first part of our analysis uses the wavelet method to compare the QuantumChromodynamic (QCD) prediction for the ratio of hadronic to muon cross sectionsin electron-positron collisions, $R$, with experimental data for $R$ over acenter of mass energy range up to about 7 GeV. A direct comparison of the rawexperimental data and the QCD prediction is difficult because the data have awide range of structures and large statistical errors and the QCD descriptioncontains sharp quark-antiquark thresholds. However, a meaningful comparison canbe made if a type of "smearing" procedure is used to smooth out rapidvariations in both the theoretical and experimental values of $R$. A waveletanalysis (WA) can be used to achieve this smearing effect. The second part ofthe analysis we concentrate on the 3.0 - 6.0 GeV energy region containing therelatively wide charmonium resonances $\psi(1^-)$. We use the waveletmethodology. Both analyses are examples of the usefulness of WA in extractinginformation in a model independent way from high energy physics data.

Using wavelet analysis to compare the QCD prediction and experimental  data on $R_{e^+e^-}$ and to determine parameters of the charmonium states  above the $D\bar D$ threshold