Aperiodic Signals

Abstract

In the previous chapter we have seen how a periodic signal may be expressed as the sum of a set of sinusoidal waves which are harmonically related. The spectrum of such a signal consists of a number of discrete frequencies and is known as a ‘line’ spectrum. Although the analysis of periodic signals gives results which can be of great practical interest, the great majority of signals are not of this type. Firstly, even signals which repeat themselves a very large number of times are generally turned ‘on’ and ‘off’. In other words they may not generally be assumed to exist for all time past, present, and future, and it is important to understand the effects which time-limitation has upon their frequency spectra. Secondly, and quite apart from any question of time-limitation, there is an important class of signal waveforms (amongst which are included random signals) which are simply not repetitive in nature and which cannot therefore be represented by Fourier series containing a number of harmonically-related frequencies. Fortunately, however, it is possible to derive frequency spectra for such signals using as a starting point the work we have already done on the Fourier series.