In this work a new mathematical modeling approach is proposed for the representation of the speech and audio signals. This approach is based on the generation of the so called Predefined Signature Sequence (PSS) and Predefined Envelope Sequence (PES) Sets. After the generation process of the PSS and PES sets, they are clustered by effective k-means clustering algorithm and the PSS and PES are redefined by using these centroids. By using this approach, the drawbacks by means of the size of the sets, speed of the reconstruction process (computational complexity) which arise in the proposed methods previously are highly eliminated. In spite of these improvements, the initial results proved that, the quality of the reconstructed signals remains within the limitations of the acceptable hearing quality.