Analysis of digitized waveforms using Shannon entropy

Abstract

A novel symbol-oriented, information-theoretic approach to signal analysis is described based on application of Shannon entropy. It is shown that this can be a preferred alternate to conventional digital signal energy analysis by making an experimental comparison of scanned ultrasonic images formed from Shannon entropy, signal energy, and log signal energy measurements. In these images, which were made by c scanning a Plexiglas bar with drill-hole ‘‘defects,’’ the Shannon entropy exhibits approximately two to three times the sensitivity of the two energy measures. However, the Shannon entropy analysis of waveforms suffers from a severe fundamental defect. It depends on the properties of the analog-to-digital converter (ADC) used to acquire the waveform as well as the properties of the waveform itself. As digitizer dynamic range is increased the Shannon entropy ultimately saturates at a level governed by the properties of the digitizer alone. This effect arises from the necessary limited bandwidth of a real ADC; if ADC bandwidth were not limited, the Shannon entropy would grow without bound with increasing dynamic range. To overcome this difficulty, a variant of the Shannon entropy is defined that depends only on the properties of the waveform. It is then shown that this variant is sensitive to the same scattering features as is the Shannon entropy for data acquired from the Plexiglas specimen discussed initially. Furthermore, the variant offers the same sensitivity improvements obtained from the Shannon entropy analysis. Finally, computation of this variant for waveforms having noise is described. Derivation of the variant is given in Appendix A of this work. Several of its more interesting features are also discussed there. Derivation of the procedure required to compute the variant is given in Appendix B.