  A parametrized multipolar gravitational wave phasing within multipolar
post-Minkowskian and post-Newtonian formalism was developed in earlier works
[S. Kastha et al., PRD 98, 124033 (2018) & S. Kastha et al., PRD 100, 044007
(2019)]. This facilitates the model-agnostic tests for the multipolar structure
of compact binaries using gravitational wave observations. In this paper, we
derive a parametrized multipolar amplitude of the gravitational wave signal in
terms of mass and current-type radiative multipole moments within the
post-Newtonian approximation to general relativity. We assume the compact
binary to be moving in quasi-circular orbits, with component spins (anti-)
aligned with respect to the binary's orbital angular momentum. We report a
closed-form expression for the parameterized multipolar amplitude of the
waveform at second post-Newtonian order both in time and frequency domains.
This includes the contribution from the leading five mass-type and the leading
four current-type radiative moments. This framework of constructing a
parametrized waveform accomplishes a generic parametrization of both
gravitational wave phase and amplitude with the same set of phenomenological
parameters. Hence, it should significantly enhance the precision of the
multipole tests in the context of present and future gravitational wave
detectors.
