Wavelet Scale and Wavelength in Wavelet Transform

The relationship between scale and wavelength in wavelet transform is investigated. First, the definition of wavelet transform with scale-energy parameter is given, its corresponding properties in time (spatial)-frequency domain are presented. Then, the method is proposed to how to get the relationship between scale and wavelength; the relationship formulas for several commonly used wavelets are given. Finally, an illustrative example of the relationship between scale and wavelength in Morlet wavelet is presented and simulation results show the effectiveness of the proposed formulas