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

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5aren’t close enough to capture them. This is because these harmonics vibrate sofast the waves are very close together in these areas.1.2 Converting from Analog to Digital <strong>and</strong> Back toAnalog1.2.1 Analog to DigitalWhen converting analog sound into digital sound, the first step is for theAnalog-to-Digital Converter (ADC) to sample the analog sound wave itself <strong>and</strong>then select points from the sound at a set frequency. For example, the CDAst<strong>and</strong>ard sampling rate is 44.1 MHz. In other words, it takes samples of thesound wave at a rate of 44,100 samples per second. Other audio signals (suchas those created by an electronic keyboard or a synthesizer) produce audio bymeans of “digital synthesis.” Such signals start as digital audio <strong>and</strong> only undergothe second phase of conversion, going from the digital signal to the actual analogsound that is heard (Kientzle 53).After the conversion to a digital signal has taken place, one of two thingscan happen. The file can be either stored on a digital storage media or playedback. When digital sound is stored, it can be stored in a number of ways, rangingfrom a CD, a hard drive, or in flash memory. Several file formats are used tostore digital audio. CDA (the CD st<strong>and</strong>ard), WAVE, AAC, <strong>and</strong> MPEG (MP3) arethe most common file formats. These are all stored using lossy compressiontechniques, which is the reason that certain harmonics are lost in the conversionprocess as noted above.
61.2.2 Digital to AnalogIn order for the sound to be heard, the digital sound must be decoded toproduce an analog wave that is then played by speakers or other soundproducingdevices. A Digital-to-Analog Converter (DAC) is responsible for this.Unlike the ADC that samples the analog sound, the DAC samples the storeddigital file at varying bit rates. The DAC connects the points from the digital file tocreate a continuous wave that can then be played back. The DAC can use one ofthree techniques, which will be discussed here.Oversampling is the process of sampling a signal with a samplingfrequency higher than twice the frequency of the signal being sampled (Kientzle31).1.2.2.1 Definition An oversampled signal is said to be oversampled by afactor of ß, as defined by the formulaffß =2sOr asHf s = 2ßf HWhere f s is the sampling frequency <strong>and</strong> f H is the highest frequency of the signalbeing sampled (Kientzle 31).Oversampling has two notable advantages. First, the higher sampling rateused in oversampling is capable of achieving better resolution in the digital-to-
Page 1: Data Inter
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 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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