We prove that the oft-used stationary-phase method gives a very accurate expression for the Fourier transform of the gravitational-wave signal produced by an inspiraling compact binary. We give three arguments. First, we analytically calculate the next-order correction to the stationary-phase approximation, and show that it is small. This calculation is essentially an application of the steepest-descent method to evaluate integrals. Second, we numerically compare the stationary-phase expression to the results obtained by fast Fourier transform. We show that the differences can be fully attributed to the windowing of the time series, and that they have nothing to do with an intrinsic failure of the stationary-phase method. And third, we show that these differences are negligible for the practical application of matched filtering.

Theoretically, laser therapy induced tissue changes in this case occurring at and below the skin surface altering inflammatory and excitatory peripheral mechanisms noted to take place in the PHN patient. Peripheral nociceptor firing must be brought back to normal thresholds to resolve such chronic neuropathic pain and inhibit the possible central sensitization component. Anti-inflammatory cytokines, growth factors, nitric oxide, adenosine triphosphate (ATP), and other mechanisms stimulated by laser therapy as noted in medical literature may be central to the favorable response seen in this patient. Controlled clinical trials of class 4 laser therapy in the PHN patient population with similar doses would be beneficial to determine if this is an effective treatment option in PHN.