Communication Theory and Signal Processing for Transform Coding

This book is tailored to fulfil the requirements in the area of the signal processing in communication systems. The book contains numerous examples, solved problems and exercises to explain the ...
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Hilbert Transform

Pp. 167-176 (10)

Khamies M. A. El-Shennawy

Abstract

The Fourier transform is used for evaluating the frequency content of the energy signal (chapter III) and in a limiting sense the power signal (chapter V). The Fourier transform analysis provides a means of analyzing and designing the frequency selective filters for the separation of signals on the basis of their frequency content, where the frequency selectivity plays the main role in the design of the communication systems. The Hilbert transform plays the same role depending on the phase selectivity. The Hilbert transform uses the phase shifts between the signals to achieve the desired separation, where the phase angles of all components of a given signal are shifted by ±90°, the resulting function of time is known as the Hilbert transform of the signal.

Keywords:

Hilbert transform, Orthogonality, Convolution principle, Narrow band-pass signals.

Affiliation:

Arab Academy for Science and Technology and Maritime Transport. P.O.Box 1029, Alexandria, Egypt.