DCT-Compressive sampling applied to speech signals

Compressive sampling (CS)is a emerging technique with many applications on signal processing field. It states that it is possible to reconstruct a signal from a number of samples below the well-known Nyquist limit. The success of the reconstruction depends on the capability of a frontend transform to represent the signal in a sparse way. In this paper, we propose the use of the discrete cosine transform (DCT) to preprocess a speech signal in order to obtain a sparse representation in the frequency domain, and thus, we show that the subsequent application of compressive sampling can represent vowels with less information than the Nyquist sampling theorem. The reader will find that the presented material differs from other speech processing techniques, as our results could be the basis for developing compression methods using the discrete cosine transform and compressive sampling. Both techniques, traditionally used for image compression, are now proposed for speech compression.