Delta modulation (Delta-M) via second-order sliding-mode control technique

In modern data acquisition and communication technologies, the differential coding scheme known as Delta Modulation (D-M) is being rediscovered as an efficient 1-bit analog-to-digital conversion and compression technique due to its simplicity in implementation, high resolution and minimal data throughput rate. In this paper it is proposed a second-order D-M scheme based on the second-order “suboptimal” sliding mode control technique. As compared to the traditional D-M scheme, based on the first-order sliding mode control paradigm, it yields better accuracy and noise-shaping properties as well as higher signal-to-noise ratio. Various dynamical features of the proposed scheme are investigated, both in continuous and discrete time domains, and the appropriate stability conditions are derived. Finally, numerical simulations are extensively discussed to corroborate the theoretical analysis.