Relationship between Scale and Wavelength in Wavelet Transform Analysis

The relationship between scale and wavelength in wavelet transform analysis of data series is proposed. Firstly,the feature of wavelet analysis, the different definition of wavelet transform and their Fourier transform are given, then the general formula of the relationship between scale and wavelength is deduced from the property of wavelet transform. An illustrative example of Morlet wavelet is presented and the simulation results show the effectiveness of the proposed formula. Finally, the formulas of some commonly used wavelets are given.