Fourier transform, wavelets, Prony analysis: tools for harmonics and quality of power

The Fourier transform is a very useful tool for signal studies. Nevertheless there are many problems in using it; but these problems are very well known and correctly explained in literature. Wavelets are not usual in power network analysis. However, they are easy to use and give good results; the edge effects are transient and the computation time may be reasonable. Prony analysis is only found in a few papers about power networks. There are few high-performance decomposition programs. The best ones remain sensitive to noise. They require a long observation time with many samples. But, when the analysis succeed, this method is the most powerful to explain what happens in a power network transient. This paper explains as simply as possible the wavelet and the Prony analyses and shows, qualitatively, their performances and their limits