Compressive Sensing and its Application to Speech Signal Processing

Compressive sensing, often referred to as CS, is an innovative approach that heavily depends on signal sparsity. It capitalizes on the inherent sparsity of signals, enabling the recovery of original signals with a reduced number of samples, in contrast to the conventional Nyquist-Shannon sampling theorem. The CS 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. It comprises the basic study of two necessary condition of compressive sensing theory: sparsity and incoherence. CS is a novel theory that is an ideal complement and improvement to conventional signal processing. CS reduces data acquisition requirements, saving on storage, transmission, and acquisition time. CS has been applied in areas like Radar systems, sonar systems, video signal, and image processing etc. In this paper, the compressive sensing techniques are implemented on mono-audio signals and various error values are computed which can be utilized for various applications such as efficient data acquisition, IoT, Image and Video processing and sparse recovery.