双路异频欠采样压缩感知信号处理基本理论研究

压缩感知理论是一种充分利用信号稀疏性或者可压缩性的全新的信号采样理论。欠采样是其中关键的一部分，它对于采样率的选取、信号的压缩、及信号的精确恢复以均有重要意义。压缩感知会使信号估计频谱发生混叠，大多数运用中国余数定理来解模糊；由此看来中国余数定理为一种很好的解模糊方法，但是并不是所有的欠采样混叠现象全部都能用中国余数定理进行解模糊。本文基于中国余数定理提出双路异频欠采样压缩感知信号处理理论，论证了双路异频欠采样求解信号频谱位置所要满足的条件，双频采样的二复正弦信号频谱恢复条件以及双频采样多窄带信号频谱恢复条件。最后并对其进行了仿真验证说明理论的正确性。 

Research on Basic Theory of Signal Processing for Two Different Sub-sampling Frequencies Compressive Sensing

Compressive sensing is a novel sampling theory under the condition that the signal is sparse or compressible.Sub-sampling is a crucial section,which is very important for the option of sampling rates and the signal’s compression and the accuracy spectrum recovery.However,compressing sensing would make the aliasing that can utilize the China remainder theorem to anti aliasing.But not all sub-sampling aliasing can be solved by the China remainder theorem.A novel theory of compressive sensing via two different sub-sampling frequencies based on Chinese remainder theory is proposed.First the qualification for the spectrum location of the signal after Two Different Sub-sampling is discussed,and then the spectrum recovery qualification of two complex sinusoidal signals and multi-narrowband signals are given.Simulation results show the correctness of the theory.