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

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213.2 Lagrange ResultsFor our example of a perfect sound wave, the Lagrange Polynomialresults were very good. The first example, given by the picture on the followingpage demonstrates the need for a fair amount of data points however. The lightergraph represents our original sound wave, <strong>and</strong> the darker represents theinterpolating polynomial. Keep in mind that any significant deviation from theoriginal sound wave has an extremely detrimental effect to the sound (if it’s largeenough, it can even make a completely different sound than what the originalsound was).
22The next two trial runs resulted in the functions lying directly on top ofeach other when graphed using Maple, as shown in this example:From this, we discover that if enough data points are used, we can come up witha great interpolation of a perfect sound wave. However, as with the previous
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 20 and 21: 19put in perspective that it’s so
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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