Metrics and Harmonic Analysis on DNA

A mathematical algorithm to describe DNA or RNA sequences of $N$ nucleotides by a string of $2N$ integers numbers is presented in the framework of the so called crystal basis model of the genetic code. The description allows to define a not trivial distance between two sequences and to perform the Discrete Fourier Transform on a sequence. Using the definition of distance the sequence of $\beta$-globin for Homo, Gallus and Opossum are compared. The Discrete Fourier Transform for some simple examples is computed.