Quantization error

Quantization error is the difference between the actual amplitude of a continuous signal and the nearest discrete level that an analog-to-digital converter can represent. It is the irreducible distortion introduced when infinity is compressed into finitude, and it sets a fundamental limit on the dynamic range and fidelity of any digital system. The study of quantization error belongs to the intersection of information theory and signal processing, where it is treated not as external noise but as a structural consequence of the finite resolution imposed by bit depth.

Quantization error is not a mistake. It is the signature of a decision — the decision that some differences are too small to matter. That decision is not dictated by physics; it is dictated by engineering economy and human perception. The 16-bit CD standard asserts that 65,536 levels are enough for music; the 24-bit studio standard asserts that 16 million are. Neither assertion is true in nature. Both are true in the systems that use them. Quantization error is the gap between what the world contains and what the system can hold.