Structural Health Monitoring with Piezoelectric Wafer Active Sensors, 2nd Edition

Appendix A

Mathematical Prerequisites

This appendix presents several mathematical prerequisites necessary in the understanding of the book. Fourier analysis is presented starting with the Fourier series of periodic signals and followed by Fourier transform of aperiodic signals and by discrete Fourier transform. The spectrum leakage phenomenon that appears in discrete Fourier transform is investigated. The sampling theory is discussed next, followed by a presentation of the convolution of discrete and continuous time signals. The Hilbert transform is briefly reviewed. The correlation method is discussed and its use for time-of-arrival identification is illustrated. The calculation of the time-averaged product of two harmonic variables using ...