Conclusion

Wavelets are an important discovery in applied mathematics. In many fields of application where Fourier analysis was traditionally used, they have opened up an alternative path, often better adapted to the nature of the phenomena studied. They have also had the merit of fostering dialogue between different scientific communities interested in their potential.

However, it would be wrong to assume that wavelets are a panacea for every problem. For example, if you're interested in frequency drift in a sinusoidal power system, it's unlikely that wavelets are the ideal analysis tool.

Some advanced concepts, such as multi-wavelets, regularity problems, characterization of certain functional spaces, etc., could not be covered in this article. On the other hand, wavelets remain an active subject of research, continually enriched by new ideas....