Analysis of digitized waveforms using Shannon entropy. II. High-speed algorithms based on Green’s functions

An improved approach for calculating continuous waveform entropy Hc is described. This approach is based on the use of the Green’s function for the one-dimensional differential operator L[u]=u″ with boundary conditions u(1)=u(0)=0. The method is applied to data acquired from a Plexiglas block having artificial defects in order to produce an entropy image. The defect contrast obtained with the new Green’s function computation is then compared with that obtained from a previously described Fourier series approach. It is found that the new approach produces the same or higher image contrast in a time that is roughly three orders of magnitude smaller than that required by the Fourier series method. This speedup arises from two sources. The Green’s function approach has greater inherent immunity to noise, and the number of calculations required in the Green’s function approach is much smaller than the number required in the Fourier series approach.