In a subclass of Horndeski theories with the speed of gravity equivalent to
that of light, we study gravitational radiation emitted during the inspiral
phase of compact binary systems. We compute the waveform of scalar
perturbations under a post-Newtonian expansion of energy-momentum tensors of
point-like particles that depend on a scalar field. This scalar mode not only
gives rise to breathing and longitudinal polarizations of gravitational waves,
but it is also responsible for scalar gravitational radiation in addition to
energy loss associated with transverse and traceless tensor polarizations. We
calculate the Fourier-transformed gravitational waveform of two tensor
polarizations under a stationary phase approximation and show that the
resulting waveform reduces to the one in a parametrized post-Einsteinian (ppE)
formalism. The ppE parameters are directly related to a scalar charge in the
Einstein frame, whose existence is crucial to allow the deviation from General
Relativity (GR). We apply our general framework to several concrete theories
and show that a new theory of spontaneous scalarization with a higher-order
scalar kinetic term leaves interesting deviations from GR that can be probed by
the observations of gravitational waves emitted from neutron star-black hole
binaries. If the scalar mass exceeds the order of typical orbital frequencies
$\omega \simeq 10^{-13}$ eV, which is the case for a recently proposed
scalarized neutron star with a self-interacting potential, the gravitational
waveform practically reduces to that in GR.
