The main goal of Speech enhancement is to enhance the performance of speech communication systems in noisy environments. The problem of enhancing speech which is corrupted by noise is very large, although a lot of techniques have been introduced by the researchers over the past years. This problem is more severe when there is no additional information on the nature of noise degradation is available in which case the enhancement technique must utilize only the specific properties of the speech and noise signals. Signal representation and enhancement in cosine transformation is observed to provide significant results. Discrete Cosine Transformation has been widely used for speech enhancement. In this research study, instead of DCT, a hybrid technique called DCTSLT which is the combination of Discrete Cosine Transform (DCT) and Slantlet Transform (SLT) is proposed for continuous energy compaction along with critical sampling and flexible window switching. In order to deal with the issue of frame to frame deviations of the Cosine Transformations, the proposed transform is combined with Time Domain Pitch Synchronous Overlap-Add (TD-PSOLA) method. Moreover, in order to improve the performance of noise reduction of the system, a Hybrid Vector Wiener Filter approach (HVWF) is used in this study. Experimental result shows that the proposed system performs well in enhancing the speech as compared with other techniques.