Application Of Free Search Algorithm In The Optimal Design Of Digital Filters

As a basic function unit of digital signal processing, digital filter design is themain subject of research in the field of digital signal processing, it is widely used inthe field of communication, radar and so on. The traditional design method is difficultto satisfied high performance requirements of digital filter, particularly the design ofspecial filters. Now, many scholars introduce intelligent algorithms to optimize thedesign of digital filter. This paper mainly uses Free Search algorithm to optimize thedesign of digital filter coefficients which can be satisfied different performancerequirements. The main works are carried out as follows:1)The development and application of Free Search algorithm and digital filteroptimally design are introduced. The characteristics of Free Search Algorithm areanalyzed. The search radius is the key performance and efficiency of the Free Searchalgorithm.The search radius of fundamental Freed Search algorithm is constant value.The smaller radius is the larger computation, it impacts the algorithm efficiency. Thelarger radius value is the earlier convergence, it impacts the algorithm performance.According to the characteristics of the digital filter, improved the Free Searchalgorithm, firstly by linear assignment of the search radius, ensuring large searchradius ranges, then the radius reduces by index to improve the convergence rate forensuring global optimization. In order to avoid early convergence in the optimizationprocess, the algorithm is searched by regular axial search.2)A suitable constraint on the parameters spaces is presented and theoptimization model is established under minimizing mean square error andminimizing the ripple magnitudes of both passband and stopband optimality criteria,designing IIR digital low-pass filter based on the Improved Free Search algorithm,compared with the existing methods, the superiority and the effectiveness ofImproved Free Search algorithm by simulation results. Expand the application fieldsof Free Search Algorithm.3)Based on the improved Free Search algorithm, it finds the best values throughthe transitional zone to obtain the maximum stop-band attenuation of the FIR digitalfilter. Compared with traditional design methods, the proposed method is betterperformance of its simple design and easier to operate.4)The poles of multiple notch filters are optimized by the improved Free Search algorithm. The traditional design method is not sure the symmetry of the pass-bandand transition-band gain, and uncontrollable gain at frequency DC, π and frequencybetween the notch frequencies. A novel design approach of digital multiple notchfilters is proposed based on Free Search algorithm. Firstly, improve the systemstructure to compensate magnitude of transition-band. Secondly, through optimal poleplacement, this method can realize the optimized design of notch filters with stablecharacteristics. The effectiveness and practicability of the presented method areverified with simulation experiments.The method proposed in this paper for the design of digital filter by Free Searchalgorithm is significance in both theory and engineering, it is a new approach.