Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

Complex Amplitude

Note that the amplitude $ A$ and phase $ \phi$ can be viewed as the magnitude and angle of a single complex number

$\displaystyle {\cal A}\isdefs A e^{j\phi}
$

which is naturally thought of as the complex amplitude of the complex sinusoid defined by the left-hand side of either Eq.(1.9) or Eq.(1.10). The complex amplitude is the same whether we are talking about the continuous-time sinusoid $ A e^{j(\omega t+\phi)}$ or the discrete-time sinusoid $ A e^{j(\omega
nT+\phi)}$ .


Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]

``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition)
Copyright © 2023-09-17 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA