How to interpret results of stationary phase approximation in GW case? As time increases, the amplitude and frequency of the GW signal also increase. But after using the stationary phase approximation, the signal is proportional to ${1/f^{7/6}}$, where $f$ is the GW frequency. Which means as you increase the frequency, the signal amplitude will decrease. This seems opposite to time domain signal behavior.
Can somebody please tell me what I am missing?
 A: When looking at waveforms in the frequency domain, the natural quantity to work with is the power spectrum.  This is related to the energy emitted at each frequency.
The emitting system does not spend the same amount of time at each frequency.  The system evolves more slowly at low frequencies, so more energy is emitted in the lower "frequency bins".
Take a look at figure 1 from this LIGO paper summarizing the detections of the first Advanced LIGO observing run (O1):

The stationary phase approximation accounts for the early inspiral of the waveform.  This is the powerlaw at low frequencies (left panel).  Near merger, the instantaneous amplitude grows more rapidly and the spectrum tips up.  Most of the energy is still emitted at early times, but power (energy / time) peaks near merger when the system is undergoing its most extreme evolution.  After merger the waveform decays away.
You may be interested in more sophisticated frequency domain approximations like this phenomenological model from Khan, et al.  In particular check out section V.C for the higher order amplitude modeling.
