An empirical envelope estimation algorithm

Envelope is the vital part of one-dimensional data. The estimation of envelope can be treated as a demodulation problem. However, the definition of envelope is ambiguous and lack of an exact mathematical definition. It is commonly agreed that envelope varies slowly and in some empirical view it should pass the prominent peaks of the data smoothly. In this study, we propose an algorithm to directly use the prominent peaks and finally get the envelope by interpolation. We term it as empirical envelope estimation algorithm (EEEA). Envelope derived by EEEA has steerable smoothness and is adaptive to the data. It has clear physical meaning and has great potential in some off-line signal analysis applications, such as musical sound analysis and heart sound analysis.