Canonic Goertzel algorithm and drawbacks of various Goertzel algorithm formulations

This paper shows that the Goertzel algorithm derivations, which over years can be found in the literature, are either inadequate or inelegant, or even erroneous. Furthermore, the resulting algorithm is noncanonic with respect to the number of recursions. In this paper a canonic formulation of the Goertzel algorithm and the so-called canonic reversed algorithm is proposed. We are convinced that the presented considerations put the problem of the Goertzel algorithm derivation/formulation in order and make it more practical, clear, and intuitive.