Chapter 32 Further Reading: Digital Audio — Sampling, Quantization & the Nyquist Theorem

Foundational Mathematics and Signal Theory

Shannon, Claude E. "Communication in the Presence of Noise." Proceedings of the IRE, 37/1 (1949): 10–21. Shannon's original paper containing the sampling theorem in its modern form. Remarkably readable for a paper of this importance. Freely available through IEEE Xplore.

Nyquist, Harry. "Certain Topics in Telegraph Transmission Theory." AIEE Transactions, 47 (1928): 617–644. Nyquist's foundational contribution on bandwidth and information transmission. More electrical engineering than pure mathematics, but historically important.

Proakis, John G., and Dimitris Manolakis. Digital Signal Processing: Principles, Algorithms, and Applications, 4th ed. Prentice Hall, 2007. The standard graduate-level DSP textbook. Chapters 4–6 cover sampling, quantization, and filter design with full mathematical rigor. Essential for readers who want the complete mathematical treatment.

Oppenheim, Alan V., and Ronald W. Schafer. Discrete-Time Signal Processing, 3rd ed. Prentice Hall, 2010. Another standard graduate DSP text. Particularly strong on the mathematics of sampling, reconstruction, and the z-transform.

Digital Audio Engineering

Pohlmann, Ken C. Principles of Digital Audio, 6th ed. McGraw-Hill, 2010. The definitive reference for audio engineers working with digital systems. Covers ADC/DAC architecture, sampling theory, quantization noise, dithering, and error correction in depth accessible to non-mathematicians.

Watkinson, John. The Art of Digital Audio, 3rd ed. Focal Press, 2001. Excellent companion to Pohlmann, with particularly good coverage of the history of digital audio development and practical engineering applications.

Dunn, Julian, and Ian Dennis. "Psychoacoustic Noise Shaping." Proceedings of the AES 106th Convention, 1999. Technical paper on noise-shaped dithering: the theoretical basis and practical implementation of perceptually optimal dither for 16-bit audio delivery.

Research Papers on Perceptual Audio Quality

Meyer, E. Brad, and David R. Moran. "Audibility of a CD-Standard A/DA/A Loop Inserted into High-Resolution Audio Playback." Journal of the Audio Engineering Society, 55/9 (2007): 775–779. The most cited paper in the high-resolution audio debate. Their double-blind tests found no statistically significant preference for high-resolution audio over 16/44.1 in controlled conditions. Essential reading for evaluating hi-res audio claims.

Reiss, Joshua D. "A Meta-Analysis of High Resolution Audio Perceptual Evaluation." Journal of the Audio Engineering Society, 64/6 (2016): 364–379. A meta-analysis of many perceptual tests of high-resolution audio, finding a small but statistically significant advantage for hi-res across multiple studies. Provides important context for the Meyer-Moran result.

Ashihara, Kaoru, et al. "Detection Threshold for Tones Above 22 kHz." Journal of the Acoustical Society of America, 116/1 (2004): 584–592. Investigation of whether human hearing extends meaningfully above 20 kHz. Relevant to evaluating claims about high-resolution audio.

Vinyl Physics and the Format Debate

Grundy, James. "Vinyl vs. Digital: A Physical Analysis." Journal of the Audio Engineering Society, 53/5 (2005): 396–408. Technical analysis comparing the measurable physical characteristics of vinyl and CD audio, with discussion of the subjective preferences that sometimes contradict the measurements.

Sterne, Jonathan. MP3: The Meaning of a Format. Duke University Press, 2012. Cultural history of the MP3 format. The chapter on the MPEG psychoacoustic model is unusually clear for a humanities text on a technical topic. Also provides useful historical context for the vinyl renaissance.

History and Cultural Context

Katz, Mark. Capturing Sound: How Technology Has Changed Music. University of California Press, 2010. Excellent cultural history of how recording technology has shaped musical practice. Chapter 7 ("Music in 1s and 0s") addresses the digital revolution specifically.

Bull, Michael. Sound Moves: iPod Culture and Urban Experience. Routledge, 2007. Sociological study of how the iPod (and by extension, MP3 culture) changed urban listening practices. Relevant to the vinyl renaissance discussion — why physical media matters beyond audio quality.

Online Resources

Xiph.org — A Digital Media Primer for Geeks Free online video tutorial by Monty Montgomery (creator of the Ogg Vorbis codec and Opus codec) that provides the most intuitively clear explanation of sampling, quantization, and Nyquist theory available anywhere. Highly recommended before or after reading this chapter. Available at: https://xiph.org/video/vid1.shtml

Hydrogen Audio Forums (hydrogenaud.io) Community forum with extensive, technically rigorous discussion of digital audio formats, codecs, and quality issues. Archive of ABX (double-blind) listening test results across many formats and bitrates.

AES Online Library (aes.org) The Audio Engineering Society's digital library contains thousands of technical papers on all aspects of audio, including many relevant to the topics in this chapter. Many older papers are freely accessible.

For the Mathematically Inclined

Jerri, A.J. "The Shannon Sampling Theorem — Its Various Extensions and Applications: A Tutorial Review." Proceedings of the IEEE, 65/11 (1977): 1565–1596. Comprehensive review of the sampling theorem and its generalizations. For readers who want the mathematical depth beyond this chapter's intuitive treatment.

Gray, Robert M. "Quantization Noise Spectra." IEEE Transactions on Information Theory, 36/6 (1990): 1220–1244. Technical treatment of the statistical properties of quantization noise, including the conditions under which quantization noise can and cannot be modeled as white noise.