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

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23section, no sound wave is exactly perfect save a single constant steady musicalnote, thus these results aren’t accurate to model most sounds.In testing the imperfect sound file, I found the interpolation to behaveerratically. As mentioned in the previous chapter, the higher the degree thepolynomial, generally the higher the absolute maxima <strong>and</strong> minima become. Thisis demonstrated by the following image, where the darkler line is the actualsound wave, <strong>and</strong> the lighter line is the interpolating polynomial:3.3 Cubic Spline ResultsFor results of the perfect sound wave, refer to the above section 3.2, asthe results were identical to that of performing polynomial interpolation on thewave.For the imperfect sound wave using the first method, overall the resultswere fairly good, though there are still some areas where the error is quite large.
24The following picture shows this, where the wave is dark <strong>and</strong> the interpolant islight.For the second method of doing Cubic Splines (which only two points areused <strong>and</strong> the second derivatives are equated), we got much more accurateresults still. The cubics were much closer to the original wave (as I hadsuspected would happen), though there is still some deviation in some spots.Nonetheless, given the graphical interpretation, this could dramatically improvesound quality in certain spots. However in others it might not have as mucheffect. The darker wave is the sound wave, <strong>and</strong> the lighter is the interpolant:
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 22 and 23: 213.2 Lagrange ResultsFor our examp
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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