Linearization of the product polar quantizer for A/D conversion of measurement signals

In this paper, the linearization of product polar quantizers is presented. Product polar quantizers are very important in A/D (analogue-to-digital) conversion and compression of measurement signals with Gaussian distribution, as they have much better performances than scalar quantizers and can be widely used in many modern measurement systems such as telemetry, telemedicine, wireless sensor networks, distributed measurement systems and remote control systems. The key limiting factor in the realization of product polar quantizers is the fact that the companding function for the magnitude quantization is non-linear. To decrease complexity of realization of product polar quantizers, we suggest the linearization of the companding function. Two methods of linearization are proposed. Although both methods are good, we highlight the second method, which achieves high performances with a small number of linear segments, due to optimization of the last linear segment. The convergence of expressions for the distortion before and after linearization is proved. The analysis is developed in the general manner (for any companding function) and applied on a µ-law companding function. The influence of linearization on the robustness of product polar quantizers is analysed. The best solutions for the design of the linearized product polar quantizers, considering complexity and quality, are proposed. The linearization of product polar quantizers compatible with the widely used G.711 standard is performed. It is shown that linearized product polar quantizers, although much simpler, can achieve performances very close to those of the corresponding non-linearized quantizers. Theory is proved by the simulation and experiment.