Indexed in: Book Citation Index, Science Edition.
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*(Excluding Mailing and Handling)
Pp. 103-112 (10)
Khamies M. A. El-Shennawy
Fourier series analysis is performed to obtain the discrete spectrum representation of a given periodic signal (power signal) xp(t) which has finite periodic time T_{o} , finite average power and infinite energy, to describe its frequency components content (n/T_{o}), where n = 0, 1, 2, 3, 4, ... , by either using the real coefficients method to obtain the real coefficients a_{n} and b_{n}, Equations (2.2) and (2.3), to construct x_{p}(t), Eq.(2.1), or by using the complex coefficient method to obtain the complex coefficient C_{n} , Eq.(2.13) to construct the real value of x_{p}(t), Eq.(2.12), (chapter II). While Fourier transform analysis is performed to obtain the continuous spectrum representation of a given unperiodic signal (energy signal) x(t) which has infinite periodic time T_{o} , finite energy, and zero average power (chapter III). Fourier transform is also used in a limiting sense, to evaluate the frequency content of the periodic signal x_{p}(t). Moreover, there are some special periodic functions cannot be solved using Fourier series analysis such as the periodic Dirac delta function, in this case, Fourier transform is the only way to evaluate its frequency content.
Spectral Analysis, Fourier transform, Power spectra, Periodic signals.
Arab Academy for Science and Technology and Maritime Transport. P.O.Box 1029, Alexandria, Egypt.