Phasor and Carrier Components of Sinusoids

Chapter Contents:

Search Mathematics of the DFT

Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?

If we restrict in Eq. $\,$ (4.10) to have unit modulus, then $\sigma=0$ and we obtain a discrete-time complex sinusoid.

$\displaystyle x(n) \isdef z_0 z_1^n = \left(Ae^{j\phi}\right) e^{j\omega n T} = A e^{j(\omega n T+\phi)}, \quad n=0,1,2,3,\ldots \protect$

(4.11)

where we have defined

$\begin{eqnarray*} z_0 &\isdef & Ae^{j\phi}, \quad \hbox{and}\\ z_1 &\isdef & e^{j\omega T}. \end{eqnarray*}$

Previous: Powers of z
Next: Phasor

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.

Sign in