  In this work, we present a consistent Hamiltonian analysis of cosmological
perturbations for generalized non-canonical scalar fields. In order to do so,
we introduce a new phase-space variable that is uniquely defined for different
non-canonical scalar fields. We also show that this is the simplest and
efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach
of [arXiv:1512.02539] to non-canonical scalar field and obtain a new definition
of speed of sound in phase-space. In order to invert generalized phase-space
Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a
general inversion formulae and show that our approach for non-canonical scalar
field is consistent. We also obtain the third and fourth order interaction
Hamiltonian for generalized non-canonical scalar fields and briefly discuss the
extension of our method to generalized Galilean scalar fields.
