Positive B-splines used as Mappings in the Probabilistic Quantizer

A Dithered quantizer consists of an external signal called Dither added to the input signal prior to quantization to control the statistical properties of the quantization error. In the framework known as Quantum Signal Processing (QSP) an equivalent quantizer was developed, called probabilistic quantizer, which is able to generate a Dither signal with an arbitrary joint probability distribution. This paper demonstrates how positive B-spline functions can be used as a mapping in the probabilistic quantizer and the mathematical advantages to perform their analysis. In addition, we established a relation between the order of the B-spline and the rendering of conditional moments of the error. Experimental results show that the proposed approach performs on par with Dither quantizer, and its implementation is easier.