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变换域函数空间下周期非均匀积分与重构方法

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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
投稿时间:2019-03-17
DOI:10.15918/j.tbit1001-0645.2019.055
中文关键词:线性正则变换函数空间周期非均匀积分紧支撑合成函数
English Keywords:linear canonical transformfunction spacesperiodically nonuniform averagingcompactly supported synthesizing functions
基金项目:
作者单位E-mail
王卫江北京理工大学 信息与电子学院, 北京 100081王佳童(1991-),男,博士生,E-mail:jiatong.wang.bit@gmail.com.
蔡雪滢北京理工大学 信息与电子学院, 北京 100081
王佳童北京理工大学 信息与电子学院, 北京 100081
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中文摘要:
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.
English Summary:
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.
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