Signals and Systems

2

Fourier Series

Sinusoidal quantities can be generated very easily. Sometimes the excitations are non-sinusoidal in nature and it may be periodic or non-periodic i.e., aperiodic. If f(t) = f(t + T), the function f(t) is called periodic having time period T. In 1822, the French mathematician J. B. J. Fourier had first studied the periodic function and published his famous theorem. It states that any periodic signal can be resolved into sinusoidal components. Fourier series is the resulting summation of a harmonic sinusoid. The signal may be in time domain or in frequency domain. Fourier series can be represented either in the form of infinite trigonometric series or in the form of infinite exponential series. There are DC terms as well as AC ...