Introduction to Spectral and Correlation Analysis: Basic Measurements and Methods

Abstract

Spectral analysis is one of the most important tools used in experimental structural dynamics. This can be partly explained by the fact that the output of a linear system in the frequency domain, at each frequency, is equal to the product of the input spectrum at that frequency and the frequency response at the same frequency. For random vibrations, correlation functions and their frequency counterparts, spectral densities, are the tools used to describe the frequency content of the vibrations. In this chapter, we start by briefly describing the essential properties of linear systems. After this, we describe the three classes of signals: periodic, random, and transient signals, and for each signal class, we define a spectrum to describe its frequency content. We then go on to describe the discrete Fourier transform, DFT, since this is by far the most common tool to compute spectra, by the fast Fourier transform (FFT) algorithm. In this context, leakage and time windowing are explained, after which we go into detail on how to compute the spectra for each type of signal. Two different methods are described: Welch’s method, based on averaging several shorter DFT blocks, and the periodogram-based method which relies on making one, long DFT and then averaging adjacent frequency bins. Finally, also correlation function estimates are described using the same two techniques.