Convolution and correlation: A case study of scanning imaging and analysis systems

Abstract

Summary:The relationship between convolution / correlation operation and the data acquisition process of the scanning microscope and spectrometer families is analyzed. It is shown that a coordinate or event sensitive detector, and the intrinsic or extrinsic property of the specimen response, are two important factors in distinguishing the data acquisition mode of such systems. Four types of convolution-and correlation-based modes are extracted to illuminate the physical characteristics of scanning imaging and analysis systems by focusing on the probe, specimen, detector, and their relationships. Criteria for identifying these modes are explored. In addition, the physical meanings of general existing coefficients between the independent variables of convolution and correlation are investigated.

Analysis of Vibration and Acoustic Signals for Noncontact Measurement of Engine Rotation Speed

“…According to Appendix A and characteristic of correlation [26,27], R 1 >> R 2 + R 3 , the frequency spectrum function of the correlation sequence is simplified as below:…”