Skalaarikvantointi

Skalaarikvantointi, also known as scalar quantization, is a fundamental technique in digital signal processing and data compression. It involves mapping a continuous or large set of discrete input values to a smaller, finite set of output values. This process effectively reduces the number of bits required to represent the original data, leading to compression.

The core idea of scalar quantization is to divide the range of possible input values into several intervals or bins. Each interval is then associated with a single representative value, often referred to as a codeword or quantization level. When an input value falls within a specific interval, it is replaced by the codeword for that interval. This replacement introduces a small amount of error, known as quantization error or distortion, because the original value is not perfectly preserved.

The performance of a scalar quantizer is typically measured by its rate (the number of bits per sample) and its distortion. The goal is to minimize distortion for a given rate or to achieve a target distortion with the lowest possible rate. Common methods for designing scalar quantizers include uniform quantization, where the intervals are of equal size, and non-uniform quantization, where the interval sizes are adjusted based on the probability distribution of the input signal. Non-uniform quantization is often more efficient for signals with a non-uniform probability distribution, as it allocates more quantization levels to regions where the signal is more likely to occur.

Scalar quantization is a building block for more complex compression schemes, such as those used in audio and image compression. While it alone can achieve some level of compression, its principles are extended and combined with other techniques to achieve higher compression ratios.