Kvantiseerimisviga

Kvantiseerimisviga, or quantization error, is a concept in digital signal processing and numerical analysis that refers to the discrepancy introduced when a continuous range of values is approximated by a finite set of discrete levels. This error occurs during the process of analog-to-digital conversion, where an analog signal is sampled and represented digitally.

In practice, when an analog signal is converted into a digital form, the amplitude of the signal at each sampling point is rounded to the nearest available digital level. Due to this rounding, the difference between the actual signal value and its quantized approximation is known as the quantization error or kvantiseerimisviga. The magnitude of this error depends on the resolution of the digital system, typically determined by the number of bits used to represent each sample. Higher bit depths reduce the quantization error, resulting in more precise digital representations.

Quantization error introduces noise into the digital signal, commonly referred to as quantization noise. While often considered undesirable, it can sometimes be managed or minimized through techniques such as dithering, which adds a small amount of noise to smooth out the error.

Understanding kvantiseerimisviga is essential in designing systems that require accurate digital representations of analog signals, such as audio processing, telecommunications, and image compression. The concept also plays a significant role in the analysis of errors in numerical computations involving finite precision arithmetic.

Overall, kvantiseerimisviga is fundamental in balancing the trade-off between system complexity, data size, and signal fidelity in digital systems.