Kvantifisering

Kvantifisering is a term used in several disciplines to describe the act of turning a continuous or variable quantity into a discrete form. In mathematics and logic, kvantifisering refers to the operation of binding a variable with a quantifier, such as universal quantification (for all) and existential quantification (there exists). The usual notation uses symbols ∀ and ∃, and the scope of a quantifier determines which statements depend on the bound variable. For example, ∀x (P(x) → Q(x)) asserts that all x with property P also have property Q. Quantification is fundamental to formal reasoning, definitions, and proofs.

In signal processing and computer science, kvantifisering describes the process of quantization: mapping a continuous range of values to a finite set of levels. This is central to analog-to-digital conversion, where a waveform is sampled and each sample is assigned a discrete level. Key parameters include the number of levels (often 2^n for n-bit systems), quantization step size, and quantization error or noise. Uniform quantizers assign evenly spaced levels, while nonuniform quantizers allocate more levels where the signal is denser, improving accuracy for certain distributions.

In physics, kvantifisering describes the emergence of discrete states in nature, such as energy levels in atoms or angular momentum, a concept introduced by early quantum theory. This discrete nature contrasts with the classical view of continuous spectra and has profound implications for spectroscopy, chemistry, and materials science.

The term thus covers both logical and numerical discretization concepts, linked by the idea of replacing a continuous or broad set with a countable, distinct collection.