Compressive sampling is an emerging technique that promises to effectively recover a sparse signal from far fewer measurements than its dimension. The compressive sampling theory assures almost an exact recovery of a sparse signal if the signal is sensed randomly where the number of the measurements taken is proportional to the sparsity level and a log factor of the signal dimension. Encouraged by this emerging technique, this thesis briefly reviews the application of Compressive sampling in speech processing. It comprises the basic study of two necessary condition of compressive sensing theory: sparsity and incoherence. In this thesis, various sparsity domain and sensing matrix for speech signal and different pairs that satisfy incoherence condition has been compiled.-Compressive sampling is an emerging technique that promises to effectively recover a sparse signal from far fewer measurements than its dimension. The compressive sampling theory assures almost an exact recovery of a sparse signal if the signal is sensed randomly where the number of the measurements taken is proportional to the sparsity level and a log factor of the signal dimension. Encouraged by this emerging technique, this thesis briefly reviews the application of Compressive sampling in speech processing.　It comprises the basic study of two necessary condition of compressive sensing theory: sparsity and incoherence. In this thesis, various sparsity domain and sensing matrix for speech signal and different pairs that satisfy incoherence condition has been compiled.