**NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW
VERSION:** "Mathematics of the Discrete
Fourier Transform (DFT), with Audio Applications --- Second
Edition", by Julius
O. Smith III, W3K
Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright ©
*2017-09-28* by Julius O. Smith III -
Center for Computer Research
in Music and Acoustics (CCRMA), Stanford University

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## Circular Motion

Since the modulus of the complex sinusoid is constant, it must lie on a

circlein the complex plane. For example,

traces outcounter-clockwisecircular motion along the unit circle in the complex plane, while

isclockwisecircular motion.We call a complex sinusoid of the form , where , a

positive-frequency sinusoid. Similarly, we define a complex sinusoid of the form , with , to be anegative-frequency sinusoid. Note that a positive- or negative-frequency sinusoid is necessarily complex.

REMARK: Add figure: circular motion (animation for web version)