Mathematics of the Discrete Fourier Transform (DFT)
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Triangle Inequality
The triangle inequality states that the length of any side of a triangle is less than or equal to the sum of the lengths of the other two sides, with equality occurring only when the triangle degenerates to a line. In
, this becomes
We can show this quickly using the Schwarz Inequality.
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| "Music 320 Background Reader" by Julius O. Smith III, (Course Background Reader, Music 320). Copyright © 2001-01-02 by Julius O. Smith III. - Center for Computer Research in Music and Acoustics (CCRMA), Department of Electrical Engineering, Stanford University. This is a modified HTML version reproduced by permission. |
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