DCKTKT: A New Discrete Cosine-Krawtchouk-Tchebichef Transform

Real-world signals are often intricate and difficult to analyze. Therefore, to facilitate the analysis of signal components, the researchers represent the signal in different domains (transform domain), providing a new perspective and offering significant advantages in understanding the various components of signals. Therefore, discrete transforms have been the subject of extensive study. In this paper, a new hybrid form of orthogonal polynomial is introduced named discrete Cosine-Krawtchouk–Tchebichef transform (DCKTKT). Which is based on combining discrete Cosine transform with krawtchouk and tchebichef polynomials. The mathematical and theoretical formulations of DCKTKT are presented, followed by an evaluation of its performance against other hybrid forms. The results demonstrate that DCKTKT along with their corresponding moments. Surpasses existing hybrid polynomials regarding energy compaction. Additionally, a face recognition application is performed and by using a well-known database with clean and noisy environments, DCKTKT is used to transform face images into the moment domain to facilitate feature extraction. illustrating the proposed polynomial's robustness against different types of noise and its superior feature extraction capabilities compared to the latest hybrid forms.