Chapter 5

Fourier Transform and Power Spectra

Khamies M. A. El-Shennawy

Abstract

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<sub>o</sub> , finite average power and infinite energy, to describe its frequency components content (n/T<sub>o</sub>), where n = 0, 1, 2, 3, 4, ... , by either using the real coefficients method to obtain the real coefficients a<sub>n</sub> and b<sub>n</sub>, Equations (2.2) and (2.3), to construct x<sub>p</sub>(t), Eq.(2.1), or by using the complex coefficient method to obtain the complex coefficient C<sub>n</sub> , Eq.(2.13) to construct the real value of x<sub>p</sub>(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<sub>o</sub> , 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<sub>p</sub>(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.

Total Pages: 103-112 (10)

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