Fourier series provides a method of analysing periodic functions into their constituent components. Alternating currents and voltages, displacement, velocity and acceleration of slider-crank mechanisms and acoustic waves are typical practical examples in engineering and science where periodic functions are involved and often requiring analysis.
A function f (x) is said to be periodic if f (x + T ) = f (x) for all values of x, where T is some positive number. T is the interval between two successive repetitions and is called the period of the functions f (x). For example, y = sin x is periodic in x with period 2π since sin x = sin (x + 2π) = sin (x + 4π), and so on. In general, if y = sin ωt then the period of the waveform is 2π/ω. The function shown in Fig. 69.1 is also periodic of period 2π and is defined by: