Compressive sampling is an evolving technique that promises to effectively recover a sparsesignal from far fewer measurements than its dimension. The compressive sampling theoryassures almost an exact recovery of a sparse signal if the signal is sensed randomly where thenumber of the measurements taken is proportional to the sparsity level and a log factor of thesignal dimension. Encouraged by this emerging technique, we study the application ofcompressive sampling to speech signals.The speech signal is very dense in its natural domain; however speech residuals obtainedfrom linear prediction analysis of speech are nearly sparse. We apply compressive sampling tospeech signals, not directly but on the speech residuals obtained by conventional and robustlinear prediction techniques. We use a random measurement matrix to acquire the data then use§¤-1 minimization algorithms to recover the data. The recovered residuals are then used tosynthesize the speech signal. It was found that the compressive sampling process successfullyrecovers speech recorded both in clean and noisy environments. We further show that the qualityof the speech resulting from the compressed sampling process can be considerably enhanced byspectrally shaping the error spectrum. The recovered speech quality is said to be of high qualitywith SNR up to 15 dB at a compression factor of 0.4
