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Complex and Trigonometric Identities

This section gives a summary of some of the more useful mathematical identities for complex numbers and trigonometry in the context of digital filter analysis. For many more, see handbooks of mathematical functions such as Abramowitz and Stegun [2].

The symbol $ \isdef $ means ``is defined as''; $ z$ stands for a complex number; and $ r$ , $ \theta$ , $ x$ , and $ y$ stand for real numbers. The quantity $ t$ is used below to denote $ \tan(\theta/2)$ .



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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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