The wavelet transform and its multiple versions in many aspects of the spectral analysis, the wavelet transform, likewise its relation with other transforms and special functions, needs a special treatment due to that in last years the developments in quantum electronics and recognition of signals in the frequency domain, likewise exploration profuse on new research in advanced materials like special semiconductors or fine devices in medicine, where the research is more detailed and majorly more specific in different applications. Likewise we have the wavelet transform of special function where each one can establish of very useful way the creation and design of special signal filters used in the modern industry in electronics, data processing analysis or even in the configuration of the advanced electronic equipment. Also the interphase between reception-emission devices with sensorial parts of the human body, in biomedical engineering. A version is interesting like the quantum wavelet transform which is very useful in the spectral study of traces of particles, for example studied from atomic accelerator. Finally are given general results to the discrete study of signal, which is analyzed to the wavelet transform and its spectra.