Notch Filter Design By Combining Zero Position Displacement And Kinetic-molecular Optimization

The IIR notch filter is widely used in the elimination of sinusoidal interference signals because it can be used with smaller hardware to provide a very satisfactory notch bandwidth.It is a module that is often utilized in the design of digital systems.It is widely used in communications systems,medical equipment,military electronic confrontation and other fields.For the traditional placement of zero and pole,although it is a simple configuration method,but the use of this method designed notch filter has some design defects.In the design of multiple notch filter,there are a number of parameters need to be determined.When the conventional mathematical calculation method is adopted,it is difficult to obtain the optimal result quickly.In this paper,the performance of single-frequency notch structure is improved by zero position displacement,and Kinetic-Molecular Theory Optimization Algorithm(KMTOA)is applied to the optimal design of multiple notch filter.And the performance of single-frequency notch structure is improved by combining positive feedback structure.The main work of this paper including the following parts:1)Combined with zero position displacement.On the basis of the essential two order notch filter,pole-zero doublets are added to design a new single notch structure.The influence of the new added zero on the performance of the system is analyzed,The pole angles of the two poles and the new added zero are both designed to be equal to the pole angle of the original zero,the polar radius of the new added pole are designed to be equal to the pole radius of the original pole.Furtherly,transition-band gain can be increased by adjusting the polar radius of the new added zero,which can narrow the transition zone and improve the performance of notch filter.2)In the design of multiple notch filter and multi-pole single-frequency notch filter,the number of parameters to be solved is increased.When the mathematical solution is used,the amount of computation and the time of use are increased.Combining the Kinetic-molecular theory optimization algorithm,the above two problems are transformed into the problem of solving the minimum value.In the design of multiple notch filter,by cascading improved single notch filter,optimizing the polar radius of the new added zero based on Kinetic-molecular theory optimization algorithm,this method can realize the optimized design of notch filters with stable characteristics and accelerate the calculation speed.Compared with Free Search algorithm and the Particle Swarm Optimization,the KMTOA has certainadvantages.In the design of multi-pole single-frequency notch filter,optimizing the polar radius of the new added zeros and the pole angles of the new added poles based on Kinetic-molecular theory optimization algorithm,this method can realize the optimized design of notch filters with stable characteristics and improve the performance of notch filter.3)In this new system,positive feedback structure be used to displace the pole of the notch filter,and then combined with the all-pass filter.The notch filter bandwidth of this system can be adjusted by adjusting parameter?.The gain of the pass band is maintained at 1 by adding a suitable new parameter,and this new parameter is only related to the parameters in the original notch filter.By discussing the impact of positive feedback on the system,it shows that the system has excellent performance.By combining the characteristics of the all-pass filter,the system remains stable.It is applied to the design of 2-D notch filter,which can maintain the advantages of improving the notch bandwidth,the gain of the pass band is maintained at 1,which avoids the problem of the pass band gain in the method based on the negative feedback structure.The method proposed in this paper for the design of notch filter is both theory and engineering,it has a certain significance.