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Understanding Digital Signal Processing, Third Edition by Richard G. Lyons

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Chapter Nine. The Discrete Hilbert Transform

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The discrete Hilbert transform is a process used to generate complex-valued signals from real-valued signals. Using complex signals in lieu of the real signals simplifies and improves the performance of many signal processing operations. If you’ve read about the discrete Hilbert transform in the DSP literature, you’ve probably plowed through the mathematical descriptions of analytic functions, with the constraints on their z-transforms in their regions of convergence, and perhaps you’ve encountered the Cauchy integral theorem used in the definition of the Hilbert transform. Well, the discrete Hilbert ...

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