ABSTRACT
The amplitudes of the higher- frequency sinusoids decrease fairly rapidly in most cases, so that the periodic signal can be represented in practice by a finite sum of sinusoids. Once a periodic signal is represented as a series expansion of sinusoids of different frequencies, the response of an LTI circuit to the periodic signal is the sum of the responses to the individual frequency components. Circuit responses to periodic signals are of considerable practical interest because these signals are very common. The steady-state response of an LTI circuit to a periodic signal is the sum of the responses to each component acting alone. The Fourier series expansion of periodic functions can be generalized to nonperiodic functions by means of the Fourier transform. The Fourier series expansion (FSE) of an odd periodic function does not contain an average term nor any cosine terms; its Fourier coefficients can be evaluated over half a period.
