Abtastrundung

Abtastrundung is the German term for the process of rounding after the sampling of a continuous signal or a set of data points. In signal processing it refers to the conversion of a real‑valued sample to a discrete representation, usually by applying a rounding rule such as truncation, rounding to nearest, half‑even, or stochastic rounding. The difference between the original analog value and the quantized value is called quantisation error, and the choice of rounding scheme can influence the statistical properties of the resulting digital signal. In practice, hardware devices such as analog‑to‑digital converters (ADCs) use a fixed number of bits to represent each sample, and the internal rounding behaviour is determined by the ADC architecture and the control settings. In software simulations of digital signal chains, explicit rounding functions are often applied to maintain a realistic model of hardware limitations. The term also appears in data acquisition contexts, where multiple samples from a sensor are averaged to reduce noise—each averaged value may then be rounded before storage. From a theoretical perspective, Abtastrundung is closely related to quantisation theory, the Shannon–Nyquist sampling theorem, and error analysis in numerical methods. Understanding the rounding characteristics is essential for fields such as audio engineering, telecommunications, and scientific instrumentation, where precise control over quantisation error and signal fidelity is required.