An Example Vector View

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. An Example Vector View

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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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An Example Vector View: $N=2$

Consider the example two-sample signal $x=(2, 3)$ graphed in Fig. 6.1.

Figure 6.1:A length 2 signal $x=(2, 3)$plotted as a vector in 2D space.

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

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