Kvantisaatiohäviöinä

Kvantisaatiohäviöinä, or quantization errors, refer to the inaccuracies introduced when a continuous range of values is represented by a finite number of discrete values. This process is fundamental in digital signal processing and data compression. When an analog signal, which has an infinite number of possible values, is converted into a digital signal, it must be sampled and then quantized. Sampling discretizes the signal in time, while quantization discretizes it in amplitude. The quantization step involves mapping each sampled value to the nearest available discrete level.

The difference between the original analog value and its quantized discrete representation is the quantization error. This error is inherent to the quantization process and cannot be eliminated entirely, only reduced by increasing the number of discrete levels. A larger number of quantization levels leads to a finer resolution and thus smaller errors. However, more quantization levels also require more bits to represent each value, increasing data storage and transmission requirements.

Quantization errors manifest as noise in the reconstructed signal. In audio, this can be perceived as a form of distortion. In image processing, it can lead to banding or loss of detail. The magnitude of the quantization error is typically bounded, and its statistical properties depend on the distribution of the input signal and the quantization scheme used. Various techniques, such as dithering, can be employed to spread the quantization error over a wider frequency range or to make its audible or visible effects less objectionable, effectively trading off one type of artifact for another.