基于奇异值分解的分数阶小波综合实现方法

Synthesis implementation method of fractional wavelet based on singular value decomposition algorithm

针对现有模拟小波变换实现中存在的不足,提出了一种基于奇异值分解算法的分数阶小波综合实现方法。首先,根据分数阶系统理论和介电松弛特性的Cole-Cole分布函数,构造了一种新的分数阶小波;然后,以线性离散系统的状态空间模型为基础,采用矩阵奇异值分解算法求解出分数阶小波逼近函数;最后,利用多输出开关电流双线性积分器和电流镜作为基本结构单元,设计了冲激响应为分数阶小波逼近函数的多环反馈开关电流小波滤波器。对开关电流分数阶小波滤波器的时域和频域响应以及灵敏度和非理想性进行了仿真与分析,实验结果表明所提出的分数阶小波综合实现方法具有小波逼近算法简单且逼近精度较高、电路灵敏度低和受元件非理性因素影响小等特点。

Aiming at the shortcomings of the existing analog wavelet transform methods,a novel method for implementing the fractional order wavelet（ FROW） based on singular value decomposition（ SVD） algorithm was presented. Firstly,according to fractional order system theory and Cole-Cole distribution of dielectric relaxation characteristic,a new FROW function was constructed. Then,the SVD algorithm was used to solve FROW approximation function based on linear discrete time state space model. Finally,the multiple-loop feedback switched-current（ SI）filter whose impulse response was the approximated FROW was designed using multi-output SI bilinear integrators and current mirrors as the basic building blocks. The time and frequency domain responses,sensitivity and effect to component imperfection of the SI FROW filter were simulated and analyzed in this paper. The experiment results indicate that the proposed method has the features of simple algorithm and high approximation precision,low sensitivity and low effect to component imperfections.