Data Interpolation and Its Effects on Digital Sound Quality - McMurry ...

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19put in perspective that it’s sound we’re dealing with, then the difference in theharmonics becomes very large.The next sample I used included points exactly halfway between our initial5 interpolating points. The error improved, though it’s still quite a ways off themark in several places:Notice from the previous diagram that the places that have the greatest amountof error are those places that the wave doesn’t have a very sharp incline ordecline. Shaper inclines result in smaller error.
20Lastly, using the highest sampling rate, we can obtain even greateraccuracy. This one actually did very well. The error was very minimal, as can beseen from this diagram:We conclude that with a moderate sample rating, Piecewise Linear <strong>Interpolation</strong>works reasonably well when dealing with perfect sounds. However, realistically,there are no sounds that are absolutely perfect, so it’s not possible to go by theseresults alone to interpolate sound.As for the Imperfect sound wave, Piecewise Linear did a relatively poorjob. Although not as bad as polynomial interpolation, it was still very poor. Thiscan be seen in the diagram on the following page, where the sound wave is thesmooth curve <strong>and</strong> the interpolant is the set of straight lines:
Page 1: Data Inter
Page 6 and 7: 5aren’t close enough to capture t
Page 8 and 9: 7audio conversion. Second, it has t
Page 10 and 11: Chapter 2: Data <s
Page 12 and 13: 11It’s obvious from Figure 2.1.2
Page 14 and 15: 131 1 1L x x x x x x x28 3 212-.321
Page 16 and 17: 152.3.1 Example Suppose we want to
Page 18 and 19: 172.3.3 Example Let’s return to t
Page 22 and 23: 213.2 Lagrange ResultsFor our examp
Page 24 and 25: 23section, no sound wave is exactly
Page 26 and 27: 25However, in the very high harmoni
Page 28 and 29: 27AppendicesAppendix A: Program Hea
Page 30 and 31: 29namespace Maths{namespace <strong
Page 32 and 33: 31namespace Interpolation</
Page 34 and 35: 33double dx = x - m_x[1];return m_y

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