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Example:
Going back to our simple 2D example $ x=[2, 3]$ , we can compute its norm as $ \Vert x\Vert = \sqrt{2^2 + 3^2} = \sqrt{13} =
3.6056\ldots\,$ . The physical interpretation of the norm as a distance measure is shown in Fig.5.5.

Figure 5.5: Geometric interpretation of a signal norm in 2D.
\includegraphics[scale=0.7]{eps/vec2dlen}

Figure 5.6: Length of vectors in sum.
\includegraphics[scale=0.7]{eps/vecsumdist}


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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 © 2014-10-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA