Fundamentals of Instrumentation and Measurement

Chapter 10¹

Representation and Analysis of Signals

10.1. Introduction

Generally, a physical phenomenon is observed through a signal carrying information. We want to extract this information and to convert it so it can be exploited. The signal processing tools and methods used in measuring a physical variable and the associated instrumentation depend on the exploitation that is carried out. An instrumentation chain consists of analog or digital electronic devices, according to the objectives for the analysis of the measured signals and the properties of these signals. Actually, rapid variations of high frequency signals are sometimes difficult to observe with a digital measurement chain; a purely analog measurement chain is preferable in this case. However, the development of microprocessors has meant that very sophisticated functions can be used in the processing algorithms. This means that a digital processing chain helps to solve much more complex problems than are possible for an analog processing chain.

The goal of this chapter is twofold. We will first present some basic mathematical tools necessary for analyzing analog and digital signals that are present in instrumentation chains. Then we will provide some examples of signal processing methods that can lead to adaptations, according to the applications being considered. In this chapter we will especially emphasize mathematical tools for digital signal processing and time-frequency representations that are useful for extracting ...