Modeling the Quantization Staircase Function

Quantization plays a central role in data compression. In speech systems, vector quantizers are used to compress speech parameters. In video systems, scalar quantizers are used to reduce variability in transform coefficients. More generally, quantizers are used to compress all forms of data. In most cases, the quantizers are based on some form of staircase function. Deriving an analytical expression for a uniform midrise quantizer is well known and straightforward. In this paper, we create an alternate method of deriving such an analytical expression with the hope that the steps involved will be useful in understanding quantization and its various applications.