DCT-Compressive Sampling of Multifrequency sparse audio signals

In this paper, we propose to apply the discrete cosine transform (DCT) and the compressive sampling (CS) techniques to audio signal compression. Using spectral analysis and the properties of the DCT, we can treat audio signals as sparse signals in the frequency domain. This is especially true for sounds representing tones. Thus, we propose the use of DCT as a preprocessor in order to sparsely represent a signal in the frequency domain, combined with CS to obtain an efficient representation of the signals. We show that the subsequent application of CS represents our signals with less information than the well-known sampling theorem.