9.1 Introduction

Spectral (or frequency) analysis generally serves to describe a signal in terms of its components in the frequency domain. We shall deal in this chapter only with spectra in the sense of the Fourier transform; thus, we will have in mind harmonic components of different frequencies and unlimited duration. If we can find the description of a signal in the frequency domain, i.e. magnitudes and possibly even mutual phase (or time) shifts of its harmonic components, we can make certain conclusions about the character of the signal. This may enable us to classify or to recognise the signal, to use the information to design a suitable communication channel or archiving medium for such a signal or to consider restricting information about less important components in order to compress the data describing the signal. Applications of spectral analysis are very broad; we shall meet some illustrative examples in this and further chapters. More detailed information on concrete applications, such as in the area of speech recognition, nondestructive testing in different technical fields, biomedical diagnostic applications, multimedia signal processing, telecommunications etc. can be found in specialised literature.

We meet in principle two different approaches in the field of spectral analysis: either a concrete individual signal to be analysed or a whole class of partly differing signals to be described. In the former case, description in the frequency domain, called the spectrum, should usually be so detailed as to enable complete recovery of the signal, based on spectrum knowledge. On...