Abstract
The spectral analysis, in much aspects as are the wavelet transform in its numerous versions and its relation with other transforms and special functions requires a special review, since the exploration in the frequency domain to the wavelet transform is more detailed and majorly more specific in different applications. For example, the wavelet transform of special function can be very useful to create and design special signal filters or, for example, to the interphase between reception-emission devices with sensorial parts of the human body. Also the quantum wavelet transform is very useful in the spectral study of traces of particles. Likewise, in this chapter, these aspects are considered as an inherent property of the wavelet transform in the spectral exploration of some phenomena. Finally, general results to the discrete case are given, which is analyzed to the wavelet transform and its spectra.
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