PERIODIC SIGNAL EXPANSION WITH WAVELETS ON COMPACTLY SUPPORTED INTERVAL

This paper systematically provides information for periodic signal expansion with wavelets on compactly supported interval. Basing on the fruit of generic periodic multi-resolution analysis (PMRA), the paper studies two typical cases, i.e. periodic signals with 1 period and with the finite interval, both of which are the representatives of various periodic signals on real line. It proves that the wavelet expansion of all types of periodic signals can be normalized to the framework of generic PMRA. From the application point of view, the paper also discusses several critical aspects of periodic signal expansion and reconstruction in numerical computation