一种新的窗函数法设计余弦调制滤波器组系统

摘要

针对用传统的窗函数法,设计滤波器组存在设计复杂、性能不理想等缺点,提出了一种新的余弦调制滤波器组设计方法.该方法采用了一种在理想滤波器的过渡带内插样条函数的窗函数法设计原型滤波器,放松精确重构的限制条件,将余弦调制滤波器组的设计问题转化为无约束的目标函数的优化问题;再用量子粒子群优化算法优化目标函数,求得最优参数通带截止频率,设计出有限冲激响应(finite impulse response,FIR)原型滤波器.仿真实验表明,用本文算法设计的余弦调制滤波器组在幅度失真、混叠失真、信噪比、重构误差等方面都明显优于用传统的“砖墙式”理想滤波器设计的余弦调制滤波器组,用本方法设计的余弦调制传输复用器在通信系统中的应用也有很好的性能.%In view of the critical shortcomings such as the design complexity and unsatisfactory performance of filter bank with the conventional windowing, a new approach is proposed to design a bank of prototype filtes with cosine modulated. In the proposed method, the prototype filter is optimized by using the windowing technique, with the novelty of exploiting spline functions in the transition band of the ideal filter, it relaxes the perfect reconstruction limitation, the design problem of cosine modulated filter bank is formulated as nonlinear unconstrained optimization of objection functions. Then a quantum-behaved particle swarm optimization algorithm is used to optimize objective functions, thus getting the optimal solution stopband cutoff frequency, and the prototype filter is designed. The simulation results demonstrate that the proposed method gives a better performance than the conventional design method in terms of amplitude distortion, aliasing distortion, and signal-to-noise ratio and reconstruction error, and the cosine-modulated transmultiplexer with the proposed technique has a good performance in the application of communications.