This paper shows how Hahn moments provide a unified understanding of the recently introduced Chebyshev and Krawtchouk moments. The two latter moments can be obtained as particular cases of Hahn moments with the appropriate parameter settings, and this fact implies that Hahn moments encompass all their properties. The aim of this paper is twofold: 1) To show how Hahn moments, as a generalization of Chebyshev and Krawtchouk moments, can be used for global and local feature extraction, and 2) to show how Hahn moments can be incorporated into the framework of normalized convolution to analyze local structures of irregularly sampled signals.