Heuristic Optimal Design of Multiplier-less Digital Filter

Abstract

This chapter introduces the design of multiplier-less digital filter based on Canonic Signed Digit (CSD) code. The well-known genetic algorithm (GA) is used to optimal design of the digital filter. Through the CSD coding of the filter parameters, the times of multiplication in the filtering process of a signal can be significantly reduced and then the calculation speed is increased. Among the existing heuristic algorithms, such as Particle Swarm Optimization (PSO), Differential Evolution (DE), Simulated Annealing (SA), etc., GA is the most suitable to CSD design due to its gene-wise crossover property. However, the CSD structure cannot be guaranteed by a general GA after the evolution of chromosomes. Thus in this chapter, a CSD-coded GA is introduced. The CSD-coded GA can reduce the time wasted by trials and errors during the evolution and then accelerate the training speed. Besides, a new hybrid code for the filter coefficients is proposed to improve the precision of the coefficients of a digital filter. Moreover, the design of both finite-impulse response (FIR) filter and infinite-impulse response (IIR) filter are examined. For the IIR filter, the stability problem is very important. Hence, a robust stability criterion is introduced in this chapter for the design of IIR filter.