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 means ``is defined as''; stands for a complex number; and , , , and stand for real numbers. The quantity is used below to denote .

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Subsections

• Complex Numbers
• The Exponential Function
• Trigonometric Identities
  • Trigonometric Identities, Continued
  
  
• Half-Angle Tangent Identities

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.