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This study introduces a new set of orthogonal polynomials and moments and the set's application in signal and image processing. This polynomial is derived from two well-known orthogonal polynomials: the Tchebichef and Krawtchouk polynomials. This study attempts to present the following: (i) the mathematical and theoretical frameworks for the definition of this polynomial including the modelling of signals with the various analytical properties it contains, as well as, recurrence relations and transform equations that need to be addressed; and (ii) the results of empirical tests that compare the representational capabilities of this polynomial with those of the more traditional Tchebichef and Krawtchouk polynomials using speech and image signals from different databases. This study attempts to demonstrate that the proposed polynomials can be applied in the field of signal and image processing because of the promising properties of this polynomial especially in its localisation and energy compaction capabilities.