Chapter Five: Digital Audio

### 1. Overview and Early History

**Overview**

The principles which underlie almost all digital audio applications and devices, be they digital synthesis, sampling, digital recording, or CD or iPod playback, are based on the basic concepts presented in this chapter. New forms of playback, file formats, compression, and storage of data are all changing on a seemingly daily basis, but the underlying mechanisms for converting real-world sound into digital values, manipulating those data, and finally converting them back into real-world sound, has not varied much since **Max Mathews** developed MUSIC I in 1957 at Bell Labs.

The theoretical framework that enabled musical pioneers such as Max Mathews to develop digital audio programs stretches back over a century. For the brevity of this introduction, a mention of the groundbreaking theoretical work done at Bell Labs in the mid-20th century is worth noting. Bell Labs was concerned with transmitting larger amounts of voice data over existing telephone lines than could normally be sent with analog transmissions, due to bandwidth restrictions. Many of the developments pertaining to computer music were directly related to work on this topic.

Module 4 will explore the implications of the Nyquist Theorem on the limitations of digital audio. First presented by **Harry Nyquist**, a Swedish-born physicist, in *Certain Topics in Telegraph Transmission Theory *(Trans. AIEE, vol. 47, pp. 617-644, Apr. 1928), he laid out the principles for sampling analog signals at even intervals of time and at twice the rate of the highest frequency so they could be transmitted over telephone lines as "digital" signals, even though the technology to do so did not exist at the time. Part of this work is now known as the** Nyquist Theorem**. Nyquist worked for AT&T, then Bell Labs. Twenty years later, **Claude Shannon**, mathematician and early computer scientist, also working at Bells Labs and then M.I.T., developed a proof for the Nyquist theory (thereby making it a theorem)*. The importance of their work to information theory, computing, networks and digital audio cannot be understated. For example, the same data stream theory used in high-speed networking, known as T-1 lines, is the same technology used in higher-end Digidesign Pro Tools systems today (TDM or time division multiplexing). **Pulse Code Modulation** (PCM), a widely used method for encoding and decoding binary data, such as that used in digital audio,
was also developed early on at Bell Labs, attributed to John R. Pierce, a brilliant engineer in many fields, including computer music, and others.

Competing claims for the title of the world's first computer music program exist. Not to offend our good friends down under, a mention of Geoff Hill, who programmed the CSIR MkI developed in Sydney (credited as being among the first stored program digital computers, later known as the CSIRAC) to play the Colonel Bogey March in 1951 is in order, as this seems to be the first instance of programmed computer-generated music this author can find, primitive as it may have been. For a history of the musical contributions of CSIRAC, click here.

*The Shannon Theorem ( A mathematical theory of communication, Bell System Technical Journal, vol. 27, pp. 379-423 and 623-656, (July and October, 1948)), a pioneering work in information theory, should not be confused with the Shannon Juggling Theory of the same author, in which he worked out the mathematics of juggling numerous objects ((F+D)H=(V+D)N, where F is the time an object spends in the air, D is the time a object spends in a hand, V is the time a hand is vacant, N is the number of objects juggled, and H is the number of hands)--he was an avid juggler as well.

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