Research On Frequency-domain Construction Of Analog Wavelet Filter And Switched-current Circuit Implementation

With the rapid development of information technology,wavelet transform has received extensive attention from scholars at home and abroad because of its excellent performance in signal processing in both time and frequency domains.The analog circuit implementation of continuous wavelet transform faces a series of challenges,such as real-time,accuracy,low power consumption and other requirements are difficult to meet.This thesis aims to improve the accuracy of the analog wavelet filter by studying the analog wavelet construction method and the analog wavelet filter circuit design method.The main contents are as follows:（1）Research on direct frequency domain construction method of wavelet filter based on beetle search algorithm.Aiming at the problems that the existing frequency-domain method for approximating the wavelet has low precision and does not satisfy the stability of the circuit network,a direct frequency-domain construction method is designed to solve the approximate rational expression of the wavelet function.Design a rational formula that is easy to implement in a circuit.Starting from the causal conditions that the analog wavelet filter needs to meet,the stability of the circuit network and the high precision requirements,the error value between the real and imaginary parts of the wavelet and the approximation rational formula is used as the objective function.A direct frequency domain construction model is established,and the sum of squared errors and the mean squared error are introduced as evaluation indicators.However,the wavelet approximate rational expressions in the model are complex and high-order,and the accuracy of the direct application of the beetle search algorithm is not high.Taking the commonly used wavelet as an example,this thesis introduces the greedy probability and Monte Carlo idea to improve the beetle search algorithm to solve the direct frequency domain construction model.The simulation results show that the direct frequency domain construction method of wavelet filter based on beetle search algorithm proposed in this thesis has a good effect,and the frequency domain mean square errors of Marr wavelet and Gaussian wavelet are only 7.3462×10^-4and3.4468×10^-4.（2）Research on direct frequency domain construction method of wavelet filter based on whale optimization algorithm.Although the improved long beetle search algorithm can obtain high-precision results,the method needs to reasonably set the initial parameter variables such as the initial length of the long beetle tentacles,the initial step size,and the search range.In order to find a widely applicable and simple algorithm for the direct frequency domain construction model,this thesis solves the direct frequency domain construction model based on the whale optimization algorithm with nonlinear variable convergence factor.The simulation results show that under the same conditions,the mean square error of the frequency domain approximation of the sixth-order Marr wavelet is only 7.2615×10^-4,which has a high approximation accuracy.（3）Research on the realization of multi-loop switch current circuit for simulating wavelet filter.Using bilinear mapping switch current integrator and multi-loop circuit structure,taking the sixth-order Marr wavelet obtained by the whale optimization algorithm to solve the direct frequency domain construction model as an example,the sixth-order Marr wavelet analog wavelet filter circuit is designed and implemented.Through circuit simulation experiments,it is verified that the method can realize high-precision wavelet filter and effectively reduce circuit sensitivity.To sum up,this thesis solves the wavelet direct frequency domain construction model based on the improved beetle search algorithm,improves the filter approximation accuracy,and further designs the whale optimization algorithm based on nonlinear convergence factor,which reduces the initial parameters required for the optimization solution.and the superiority of the algorithm is proved by simulation experiments.Finally,an analog wavelet filter is designed with a multi-loop switching current circuit.The experiment proves that this method can effectively reduce the sensitivity and improve the impulse response accuracy of the circuit.This thesis provides a new idea for the design and circuit implementation of the analog wavelet filter.