Various speech enhancement Algorithms (SEA) have been developed in the last few decades. Each algorithm has its advantages and disadvantages because the speech signal is affected by environmental situations. Distortion of speech results in the loss of important features that make this signal challenging to understand. SEA aims to improve the intelligibility and quality of speech that different types of noise have degraded. In most applications, quality improvement is highly desirable as it can reduce listener fatigue, especially when the listener is exposed to high noise levels for extended periods (e.g., manufacturing). SEA reduces or suppresses the background noise to some degree, sometimes called noise suppression algorithms. In this research, the design of SEA based on different speech models (Laplacian model or Gaussian model) has been implemented using two types of discrete transforms, which are Discrete Tchebichef Transform and Discrete Tchebichef-Krawtchouk Transforms. The proposed estimator consists of dual stages of a wiener filter that can effectively estimate the clean speech signal. The evaluation measures' results show the proposed SEA's ability to enhance the noisy speech signal based on a comparison with other types of speech models and a self-comparison based on different types and levels of noise. The presented algorithm's improvements ratio regarding the average SNRseq are 1.96, 2.12, and 2.03 for Buccaneer, White, and Pink noise, respectively.