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

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), with Audio Applications --- Second Edition'', by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8.
Copyright © 2014-04-21 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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