This is not the most earth-shaking of controversies, and many readers may wonder what the fuss is all about—if they wonder at all. The issue is important to both editor and readers because of the need for consistency; we’d like to use the same name for the same thing whenever it appears. But which name? In the case of the modulation technique that led to a new oversampling A/D conversion mechanism, we chose sigma-delta. Here’s why.

Ordinarily, when a new concept is named by its creators, the name sticks; it should not be changed unless it is erroneous or flies in the face of precedent. The seminal paper on this subject was published in 1962 [1][2], and its authors chose the name “delta-sigma modulation,” since it was based on delta modulation but included an integration (summation, hence Σ).

The logic behind Sigma-Delta Naming Concept

Delta-sigma was apparently unchallenged until the 1970s, when engineers at AT&T were publishing papers using the term sigma-delta. Why? According to Hauser [3], the precedent had been to name variants of delta modulation with adjectives preceding the word “delta.” Since the form of modulation in question is a variant of delta modulation, the sigma, used as an adjective—so the argument went—should precede the delta.

Many engineers who came upon the scene subsequently used whatever term caught their fancy, often without knowing why. It was even possible to find both terms used interchangeably in the same paper. As matters stand today, sigma-delta is in widespread use, probably for the majority of citations. Would its adoption be an injustice to the inventors of the technique?

We think not. Like others, we believe that the name delta-sigma is a departure from precedent. Not just in the sense of grammar, but also in relation to the hierarchy of operations. Consider a block diagram for embodying an analog root-mean-square (finding the square root of the mean of a squared signal) computer. First the signal is squared, then it is integrated, and finally it is rooted

If we were to name the overall function after the causal order of operations, it would have to be called a “square mean root” function. But naming in order of the hierarchy of its mathematical operations gives us the familiar—and undisputed—name, root mean-square. Consider now a block diagram for taking a difference (delta), and then integrat-ing it (sigma). Its causal order would give delta-sigma, but in functional hierarchy it is sigma-delta, since it computes the integral of a difference. We believe that the latter term is correct and follows precedent; and we have adopted it as our standard. - Dan Sheingold, 1990

Source: Editor- Walt Kestler, "Data Conversion Handbook", Publisher- Elsevier From "Analog Devices", ISBN - 0-7506-7841-0, Date- 2005

[1] H. Inose, Y. Yasuda, J. Murakami, "A Telemetering System by Code Manipulation -- ΔΣ Modulation", IRE Trans on   Space Electronics and Telemetry, Sep. 1962, pp. 204-209.

[2] H. Inose and Y. Yasuda, “A Unity Bit Coding Method by Negative Feedback,” IEEE Proceedings, Vol. 51, November 1963, pp. 1524–1535. (Further discussions on their 1-bit ‘delta-sigma’ concept.)

[3] Max W. Hauser, “Principles of Oversampling A/D Conversion,” Journal Audio Engineering Society, Vol. 39, No. 1/2, January/February 1991, pp. 3–26. (One of the best tutorials and practical discussions of the sigma-delta ADC architecture and its history.)