Peak finding using biorthogonal wavelets
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States), C Tan · 2000
The authors show in this paper how they can find the peaks in the input data if the underlying signal is a sum of Lorentzians. In order to project the data into a space of Lorentzian like functions, they show explicitly the construction of scaling functions which look like Lorentzians. From this construction, they can calculate the biorthogonal filter coefficients for both the analysis and synthesis functions. They then compare their biorthogonal wavelets to the FBI (Federal Bureau of Investigations) wavelets when used for peak finding in noisy data. They will show that in this instance, their filters perform much better than the FBI wavelets.