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An Example Vector View: $ N=2$

Consider the example two-sample signal $ x=(2, 3)$ graphed in Fig. 5.1.

Figure: A length 2 signal $ x=(2, 3)$ plotted as a vector in 2D space.
\scalebox{0.7}{\includegraphics{eps/vec2d.eps}}

Under the geometric interpretation of a length $ N$ signal, each sample is a coordinate in the $ N$ dimensional space. Signals which are only two samples long are not terribly interesting to hear,5.2 but they are easy to plot geometrically.


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``Mathematics of the Discrete Fourier Transform (DFT)'', by Julius O. Smith III, W3K Publishing, 2003, ISBN 0-9745607-0-7.

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Copyright © 2003-10-09 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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