  With the observational advance in recent years, primordial gravitational
waves (GWs), known as the tensor-mode cosmic perturbations, in the Loop Quantum
Cosmology (LQC) are becoming testable and thus require better framework through
which to bridge between the observations and the theories. In this work we
present a new formalism that employs the transfer functions to bring the GWs
from any epoch, even before the quantum bounce, to a later time, including the
present. The evolutionary epochs considered here include the possible
deflation, quantum bounce, and inflation. This formalism enables us to predict
more accurately the GW power spectrum today. With the ADM formalism for the LQC
background dynamics, our approach is equivalent to the commonly used Bogoliubov
transformations for evolving the primordial GWs, but more transparent for
discussions and easier to calculate due to its nature of being linear algebra
dealing with linear perturbations. We utilize this advantage to have resolved
the IR suppression problem. We also propose the field-free approximation for
the effective mass in the quantum bounce epoch to largely improve the accuracy
in the predicted GW power spectrum. Our transfer-function formalism is general
in dealing with any linear problems, and thus expected to be equally useful
under other context with linearity.
