The paper by Georgoudis, Heissenberg, and Russo explores the frequency-domain leading-order (LO) and next-to-leading-order (NLO) post-Minkowskian (PM) gravitational waveforms derived from tree-level and one-loop amplitudes describing the scattering of two massive scalar objects and the emission of one graviton. They explicitly calculate the post-Newtonian (PN) limit of these waveforms, achieving an expansion up to third subleading PN order in all ingredients: the tree-level amplitude, the odd and even parts of the real one-loop kernel, and the Compton or "rescattering" cuts. They provide explicit expressions for the multipole decomposition of these results in the center-of-mass frame and compare them with the classical Multipolar Post-Minkowskian (MPM) method. The comparison shows perfect agreement once the BMS supertranslation frame is properly adjusted and infrared divergences due to rescattering are suitably subtracted in dimensional regularization. This demonstrates that the amplitude-based approach can be applied beyond the soft regime, ensuring agreement between amplitude-based and MPM results for generic frequencies. The paper also discusses the challenges and methods used to handle spurious poles and infrared divergences in the PN expansion, providing detailed expressions for the leading and subleading corrections to the quadrupole and other multipoles.The paper by Georgoudis, Heissenberg, and Russo explores the frequency-domain leading-order (LO) and next-to-leading-order (NLO) post-Minkowskian (PM) gravitational waveforms derived from tree-level and one-loop amplitudes describing the scattering of two massive scalar objects and the emission of one graviton. They explicitly calculate the post-Newtonian (PN) limit of these waveforms, achieving an expansion up to third subleading PN order in all ingredients: the tree-level amplitude, the odd and even parts of the real one-loop kernel, and the Compton or "rescattering" cuts. They provide explicit expressions for the multipole decomposition of these results in the center-of-mass frame and compare them with the classical Multipolar Post-Minkowskian (MPM) method. The comparison shows perfect agreement once the BMS supertranslation frame is properly adjusted and infrared divergences due to rescattering are suitably subtracted in dimensional regularization. This demonstrates that the amplitude-based approach can be applied beyond the soft regime, ensuring agreement between amplitude-based and MPM results for generic frequencies. The paper also discusses the challenges and methods used to handle spurious poles and infrared divergences in the PN expansion, providing detailed expressions for the leading and subleading corrections to the quadrupole and other multipoles.