Design of FIR pulse-shaping filter: Superiority of Differential Evolution optimization over Convex optimization

Design of different types of digital FIR filter is of paramount significance in various Digital Signal Processing (DSP) applications. Different optimization techniques can judiciously be utilized to determine the impulse response coefficients of such a filter. These optimization techniques may include some conventional processes such as Convex or Non-convex optimization methods or some evolutionary algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO) or Differential Evolution (DE) techniques. In this paper, a FIR filter has been designed using Convex optimization method and the performance of the filter has been compared with that obtained by DE technique. Both the Convex optimized as well as DE optimized FIR filter has been used as a transmitting pulse-shaping filter in a Quadrature Phase Shift Keying (QPSK) modulated system to make a comparative study of the system performance. The system performance has also been compared with that of standard Raised Cosine (RC) filter. Experimental results have been included.