The Analytic Representation of Band-Pass Signals

✍ Scribed by Enrique A. González-Velasco; Emilio Sanvicente

• Publisher: Elsevier Science
• Year: 1980
• Tongue: English
• Weight: 442 KB
• Volume: 310
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(78)90013-3

✦ Synopsis

The analytic representation of band-pass signals. which is extremely useful in information transmission and radar, is usually obtained by first introducing the Hilbert transform of a signal. We consider this procedure artificial, and propose here to follow the opposite path. which leads, in a natural way, to a motivated definition of the Hilbert transform. The key to this procedure is to show how, as a simple application of the Fourier integral, every band-pass signal can be expressed as the real part of a low frequency signal which modulates an exponential. Such a representation, called the analytic signal, is then used to define the Hilbert transform in a natural manner. Finally, we show that the term analytic signal is motivated by the fact that this signal is the restriction to the real axis of a function defined and analytic (halomorphic) in the upper half of the complex plane.