ion 10.10, but the signal does The use of real and complex sinusoids to represent signals are called have many properties associated with periodic signals and cannot Fourier methods, after the mathematician who first investigated be represented by a finite number of periodic signals. these techniques. In the case of signals the Fourier representation has direct physical interpretation through measured quantities. Fou- rier analysis of signals also lends itself to automatic calculation on 10.5.3 Random and deterministic signals a computer based system. Various waveforms have Fourier series expressions. The series for Signals may be classified as random or deterministic, the deciding a general periodic wave that has an arbitrary period T is given in criteria being the predictability of a signal before it is generated. Equation 10.14, the coefficients being given by Equations 10.15 and Random or stochastic signals are those which have variations in 10.16. magnitudes that occur in an unpredictable manner. Interference and noise constitute random features of signals. If the possible future (10.14) values of a signal can be predicted from the study of previous signals then no suitable quantitative expression can be derived. Under some circumstances, following the observation of signals, a mathematical expression can be constructed to describe a wave- (10.15) form form, but there are some factors associated with parameters such as phase that are unpredictable in the first instance. A deterministic signal is one about which there is no uncertainty before it occurs and in almost all cases an explicit mathematical (10.16) expression can be written for it. The waveform depicted in Figure 10.7 has the Fourier series given by expression 10.17 with the coefficient given in Equation 10.18. 10.6 Signal representation 10.6.1 Time and frequency domains A signal x(t) may be represented in terms of sinusoids having frequencies that multiple of the fundamental frequency ficients are added to give the magnitude and phase of the sinuso