The Evolutionary algorithm is a self-adaptive searching strategy, applicable stochastic search and optimization technique based on the evolutionary theory. The algorithm maintains a population of individual solutions, each of which has a fitness value representing the quality of the solution. It adopts the operators of iterative recombination, mutation, evaluation and selection to extend the search into an undiscovered area of the search space. We investigate the phenomena of dynamics of the genetic operators and provide the contributions to the designing of the digital filters. The digital filters may be implemented via two structures: finite-impulse response (FIR) and infinite-impulse response (IIR). Typical design methods have been described in the documents of digital signal processing. And the digital filters with multiplier-free coefficients are also investigated in many studies, which have the benefit of implementation. In this work we provide several new methods to improve the quality of existing FIR/IIR designs. Moreover, the phase of the IIR digital filter will be studied and the related drawback will be improved. The contributions of this study are listed as follows: 1. The IIR digital filters with the property of minimum-phase. 2. The minimum-phase IIR digital filters with the property of linear-phase. 3. The cascade-form of multiplier-free FIR digital filters with allocation scheme. 4. The IIR digital filters with the multiplier-free coefficients and minimum-phase property. 5. The IIR digital filters with the multiplier-free coefficients and linear-phase property. The proposed linear-phase IIR filters not only improve the nonlinearity of the phase response but provide lower group delay than existing techniques. Moreover, we limit the coefficients by discrete valued (signed sum of power-of-two, SPT) to improve the implementation values. The proposed design is efficient and the related research is rare. The most similar technique first designs the infinite-precision linear-phase IIR filter and then optimizes the finite-precision linear-phase IIR filter by quantizing the coefficients by the sums of signed powers-of-two (SPT) term. This method may bring some problems. The stability, linearity of phase and the amplitude response of the IIR filter will lose control when the coefficients have been quantized. Moreover, it is difficult to look for the appropriate SPT terms to simultaneously hold the requirements of the filter. Because of the property of multi-objects, this design is difficult to achieve by conventional techniques. The proposed EA can efficiently achieve the requirements.
