变换域函数空间下周期非均匀积分与重构方法  

Periodically Nonuniform Averaging and Reconstruction of Signals in Function Spaces Associated with the Linear Canonical Transform

作　　者：王卫江[1] 蔡雪滢 王佳童 WANG Wei-jiang;CAI Xue-ying;WANG Jia-tong(School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China)

机构地区：[1]北京理工大学信息与电子学院,北京100081

出　　处：《北京理工大学学报》2020年第11期1238-1244,共7页Transactions of Beijing Institute of Technology

摘　　要：目前线性正则变换域内的周期非均匀采样理论构造的重构函数具有较高的旁瓣和缓慢衰减的速率,针对该问题,借助线性正则变换域多抽样率信号处理理论和多通道准确重建滤波器组理论,提出了基于线性正则函数空间的周期非均匀积分与重构理论.通过引入自由度较高的分段积分窗函数,该算法不仅可构造出具有紧支撑特性的重构函数,并且积分通道数不受函数空间基函数支撑区间长度的限制,更适用于只能获取有限采样点和硬件资源的实际应用场合.仿真结果表明,该算法与其他传统算法相比,可以降低插值误差,提高重构性能,减少资源开销.Several sampling theorems,which aid in the reconstruction of periodically nonuniform sampled signals in the linear canonical transform(LCT)domain,have high sidelobe and slow-decayed synthesizing functions.Focusing on this issue,the reconstruction theorem of a nonstationary signal was investigated in function spaces associated with the LCT.Periodically nonuniform averaging model and reconstruction algorithm were proposed based on the theories of multi-rate signal processing and multi-channel perfect reconstruction filter banks.Introducing window functions with high degree of freedom,the method was arranged to establish the reconstruction functions with compactly supported synthesizing capability,and to make the number of integral channel unconstrained from the range of function space,being suitable for those applications with limited sampling spots and hardware.Simulation results show that,compared with other conventional methods,the proposed method possesses the advantages with less interpolation error and fewer consumptions of hardware resources.

关 键 词：线性正则变换 函数空间 周期非均匀积分 紧支撑合成函数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]