kvantimisviga

Kvantimisviga is the difference between the input value and its quantized output in a quantization process. In digital systems it arises whenever a continuous signal is represented with a finite number of levels, such as in analog-to-digital converters, digital-to-analog converters, and fixed‑point arithmetic. The term is commonly translated as quantization error or quantization noise.

In a uniform quantizer with step size Δ, the quantization error e = x − Q(x) is bounded by −Δ/2 ≤ e ≤ Δ/2. When the input is well distributed or when a midpoint rounding rule is used, the error tends to have zero mean over time. If the input is sufficiently random or dithering is applied, the quantization error can be treated as additive white noise with variance Δ^2/12.

The step size Δ is the full‑scale range divided by the number of quantization levels, which for an N‑bit ADC is FSR/2^N. The theoretical signal‑to‑quantization‑noise ratio for a full‑scale sine wave is approximately 6.02N + 1.76 dB. In practice, the actual error depends on the input signal distribution, quantizer design (midrise vs midtread), and any pre- or post‑processing.

Impact and applications: Quantization error limits precision in measurements, reduces dynamic range, and can introduce distortion in audio, image, and video signals. In fixed‑point DSP and hardware design, accumulated rounding errors affect algorithm accuracy and stability.

Mitigation: increasing the bit depth reduces Δ and lowers error; oversampling with appropriate filtering and noise shaping can push noise out of the signal band; dithering adds controlled randomness to decorrelate the error and reduce perceptible artifacts; selecting rounding modes such as stochastic rounding or round-to-nearest helps minimize bias.