Communication Systems 9. Hilbert Transform

The quadrature filter is an all pass filter that shifts the phase of positive frequencies of a signal by -90 degrees and negative frequencies by 90 degrees. The Hilbert transform is the output of the quadrature filter to the signal. In this lecture, we define the Hilbert transform of a signal, prove its properties and solve a number of examples for demonstration. References M. P. Fitz, Fundamentals of Communications Systems, McGraw-Hill, 2007. J. G. Proakis and M. Salehi, Fundamentals of Communication Systems, Prentice Hall, 2005. J. G. Proakis and M. Salehi, Contemporary Communication Systems Using Matlab, 2nd Ed., Thomson-Engineering, 2003 S. Haykin, Communication Systems, 4th Edition, Wiley, 2000. J. D. Gibson, Principles of Digital and Analog Communications, 2nd Edition, MacMillan, 1989. M. K. Simon, S. M. Hinedi, and W. C. Lindsey, Digital Communication Techniques, Prentice Hall, 1994. R. E. Ziemer and W. H. Tranter, Principles of Communications: Systems, Modulation, and Noise, 6th Edition, Hoboken, NJ : Wiley, 2009. B.P. Lathi and Zhi Ding, Modern Digital and Analog Communication Systems, Fourth Edition, Oxford University Press, New York, 2009. L. W. Couch,II, Digital and Analog Communication Systems, 8th Edition, Pearson, 2013. Bruce Carlson, Paul B. Crilly and Janet C. Rutledge, Communication Systems: An Introduction to Signals and Noise in Electrical Communications, 4th Edition, McGraw-Hill, 2002. Nevio Benvenuto, Roberto Corvaja, Tomaso Erseghe, and Nicola Laurenti, Communication Systems: Fundamentals and Design Methods, John Wiley & Sons, 2006.

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