A short way to compute WT from STFT

Wavelet transforms are often related to Fourier transforms due to their similitude and to underline some applications where wavelet theory should be superior over Fourier analysis. Many researchers have identified that the wavelet transform (WT) maps a function analogous to the short-time Fourier transform (STFT) that has a changing size. The increase numbers of FFT dedicated devices and of previous STFT databases request for a new approach between STFT and WT. This is one of the goals of the present paper. It also suggests a possible relation between the energetic representation of these transforms. The scalogram yields a graphical representation of the signal's energy distribute over the time-scale plane, as a spectrogram distributes the energy over the time-frequency plane. So, an interesting problem, the mapping between the spectrogram and the scalogram is derived. Few examples and some computational considerations are also provided.