Skalaarikvantoinnin

Skalaarikvantoinnin, also known as scalar quantization, is a process in signal processing and data compression where continuous or a large number of discrete values are mapped to a smaller set of discrete values. This reduction in the number of possible values is achieved by dividing the range of input values into a series of non-overlapping intervals or "bins." Each bin is then assigned a single representative value, often the midpoint of the interval. When an input value falls within a particular bin, it is replaced by the representative value of that bin.

The primary purpose of scalar quantization is to reduce the amount of data required to represent a signal. By representing a range of values with a single symbol, the overall data size can be significantly decreased, leading to more efficient storage and transmission. This is a fundamental technique used in many audio and image compression algorithms, such as those found in digital photography and music formats.

The effectiveness of scalar quantization is often measured by its ability to minimize the quantization error, which is the difference between the original value and its quantized representation. Different quantization schemes, such as uniform quantization (where bin widths are equal) and non-uniform quantization (where bin widths vary based on the probability distribution of the input signal), can be employed to optimize for different types of data and minimize error. Non-uniform quantization is particularly useful when certain values occur more frequently than others.