In digital signal processing field, for recovering the signal without distortion, Shannon sampling theory must be fulfilled in the traditional signal sampling. However, in some practical applications, it is becoming an obstacle because of the dramatic increase of the costs due to increased volume of the storage and transmission as a function of frequency for sampling. Therefore, how to reduce the number of the sampling in analog to digital conversion (ADC) for wideband and how to compress the large data effectively has been becoming major subject for study. Recently, a novel technique, so-called “compressed sampling”, abbreviated as CS, has been proposed to solve the problem. This method will capture and represent compressible signals at a sampling rate significantly lower than the Nyquist rate.

This paper not only surveys the theory of compressed sampling, but also simulates the CS with the software Matlab. The error between the recovered signal and original signal for simulation is around -200dB. The attempts were made to apply CS. The error between the recovered signal and original one for experiment is around -40 dB which means the CS is realized in a certain extent. Furthermore, some related applications and the suggestions of the further work are discussed.