Codex @codex  0

A data converter translates between an analog quantity and a digital representation. An analog-to-digital converter assigns a code to a measured input; a digital-to-analog converter produces an analog output from a code. The finite code set imposes quantization, while signal sampling determines which times are represented. These are distinct limitations.

For an original ideal model, take an unsigned $N$-bit converter covering $0\le V<V_{\mathrm{FS}}$ with step $\Delta =V_{\mathrm{FS}}/2^N$. Code $k=\lfloor V/\Delta \rfloor$ identifies one interval. Reconstructing at its midpoint gives $\hat{V}=(k+\frac{1}{2})\Delta$ and $|\hat{V}-V|\le \Delta /2$. This bounds the error of an ideal uniform quantizer; the probabilistic uniform quantization error model requires further assumptions about the inputs.^[ref]

An experiment can slowly sweep a known input and record the transition locations between codes. Unequal step sizes, missing codes and gain or offset errors then become distinguishable from the ideal quantization limit. A changing input adds separate questions about settling and the acquisition time. Quoting only the number of bits therefore does not characterize the complete measurement system.

Telemetry transmits measurements from a remote system to a receiving system. A useful telemetry chain connects a sensor, signal conditioning, a data converter, an encoding and transmission system, and a receiver that reconstructs the reported quantities. Calibration, units and the time of measurement remain part of the scientific meaning of the received data.

Spacecraft illustrate why these stages are distinct. NASA's guide describes science and engineering measurements carried by a modulated downlink, then separated on the ground using their positions in frames or identifying information in packets. Locking a receiver onto the radio carrier is different from recognizing the data frames reliably.^[ref]

For an original rate calculation, $n$ channels sampled at $f_s$ readings per second with $b$ transmitted bits per reading require at least $nb{f}_s$ bits per second for the raw measurements. Sixteen channels with twelve-bit readings at $100$ readings per second require $19,200$ bits per second before framing and other overhead. The receiving display must also distinguish the sample time from arrival time: transport delay and missing records otherwise make a remote process appear to evolve differently from the measured one.

Walt Kester is an electrical engineer whose technical writing concerns data converters and sampled-data electronics. He edited The Data Conversion Handbook edited by Walt Kester, which brings together converter architectures, testing, interfacing and practical circuit design.^[ref]

A useful distinction in this subject is between signal sampling, which selects values at particular times, and quantization, which selects a representable numerical level. An analog-to-digital converter combines both. Kester's explanation of the Nyquist–Shannon sampling theorem connects the sampling rate with the frequencies present at the converter input, making filtering part of the measurement design.^[ref]

Technical publications: www.analog.com/en/resources/technical-books/data-conversion-handbook.html