Observer, Window, Mellin--Heisenberg\\and Reparametrization Covariance

Establish observer-dependent window framework with Mellin--Heisenberg phase--scale symmetry and reparametrization covariance. Core results: (i) Window choice encodes observer resolution; (ii) Mellin transform M[f](s)=\int_0^\infty f(x)x^{s-1}dx provides phase--scale representation via Weyl--Heisenberg commutation relations; (iii) Energy reparametrization E\mapsto\phi(E) induces window pushforward preserving windowed observables; (iv) Wexler--Raz biorthogonality ensures frame completeness.