摘要
提出了一种时频域混合共极点逼近的开关电流电路Morlet复小波变换方法.将Morlet复小波构成部件高斯包络进行分解,设计了高斯包络时域逼近优化模型,模型可采用常规优化算法求解.利用正弦和余弦信号的周期性,及其与指数信号的乘积在频率域具有相同极点的特性,简化了Morlet复小波函数的拉普拉斯变换,实现了实部和虚部的共极点有理逼近.基于双线性变换积分器设计了一种开关电流复二阶节基本电路,继而综合了Morlet复小波变换基本电路.通过调节基本电路的开关时钟频率可实现其它不同尺度的小波变换功能.对比分析表明,本文方法的逼近效果和系统稳定性均明显优于现有的Padé变换法和Maclaurin级数法;与现有方法相比,本文设计的复小波变换电路具有结构简单、功耗低和体积小等优点.仿真结果表明了方法的有效性.
A new scheme of implementing Morlet complex wavelet transform using poles-shared Switched--current （SI） circuits was proposed, in which a hybrid method in time and frequency domain was presented for approximation of Morlet complex wavelet. By decomposing the Gaussian envelop, which is a component of the Morlet complex wavelet, an approximation optimization model in time domain was de- signed, which can be solved in universal optimization algorithms. By using the periodic characteristics of the sine and cosine signals, the Laplace transforms of the approximated Morlet complex wavelet can be simplified. The rational real and image parts of the approximated Morlet complex wavelet have sharedpoles because the product of sine and exponential and that of cosine and exponential have same poles in s- domain. A kind of SI complex second order section circuit was designed based on the bilinear z-transform integrator module. Then it was used to synthesize the Morlet complex wavelet base circuit. By adjusting the circuit＇s switch clock frequency, the wavelet transform in other scales can be realized. The compara- tive analysis demonstrates that the proposed approximation method is better than the Pad~ transform and Maclaurin series method in accuracy and stability. Furthermore, the circuit designed has the advantages of more simple structure, lower power consumptions and smaller volumes, compared with the existing meth- od. Simulation results verified the effectiveness of the proposed scheme.
出处
《湖南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2015年第4期55-62,共8页
Journal of Hunan University:Natural Sciences
基金
国家杰出青年科学基金资助项目(50925727)
国家自然科学基金资助项目(60876022,61201108)
国防科技计划项目(C1120110004,9140A27020211DZ5102)
湖南省科技计划项目(2013GK3096)~~
作者简介
通讯联系人童耀南（1977-），男，湖南平江人，湖南大学博士研究生，湖南理工学院讲师，E-mail：yaontongl@hnu．edu．cn
