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.