Design of allpass-based IIR fullband differentiators using linear programming

Abstract

5G technology is one of the main prerequisites for the Smart Cities paradigm. 5G transceivers can notably benefit from the utilization of sophisticated signal processing techniques such as advanced digital differentiators due to the requirements for high data rates, low latency, and efficient spectrum utilization. This paper investigates the design of all-pass based infinite impulse response full band differentiators using linear programming. Obtained differentiators are optimal in the sense that relative error of the magnitude response is minimized in the Chebyshev sense. Since the starting optimization problem is non-linear, it is divided into several sub-problems that can be easily solved. As compared to existing all-pass based solutions, proposed differentiators have an additional design parameter that allows a further decrease in the magnitude response error.