基于神经网络的任意延迟M带小波设计

摘要

为了获得频率选择性更好的M带小波,提出了一种任意延时的M带余弦调制小波的优化设计方法.基于完全重构滤波器理论,通过修改系统延时参数,可以设计不同的M带双正交或正交小波.对化简为二次型的目标函数和约束条件进行参数设计时,采用增广拉格朗日乘子法将问题等价为无约束的最优化问题,提出了基于离散时间霍普菲尔德神经网络的优化设计结构.神经网络采用最速下降法做迭代运算,降低了算法的复杂度.与现有算法的实验结果相比,所提出的方法实现简单,效率高,而且优化性能更好.%In order to obtain the M-band wavelet with better frenquency selectivity,an optimum desigh method for arbitrary-delay M-band cosine-modulated wavelet was proposed.Based on the perfect reconstruction filter theory,different M-band biorthogonal and orthogonal wavelets can be designed through revising the system delay parameters.When the parameter design was performed for the simplified secondary objective function and constraint condition,an augmented Lagrangian multiplier method was used to convert the problem into an unconstrained optimization problem in an equivalent way.And an optimum design structure based on discrete time Hopfield neural network was proposed.The iterative operation was performed with steepest descent method to reduce the complexity of the algorithm.Compared with the existing algorithms,the proposed method has such advantages as simple realization,high efficiency and better optimum performance.