We investigate whether longu2011term atmospheric pressure measurements contain a coherent, frequencyu2011stable signal consistent with the expected gravitationalu2011wave (GW) emission from the eclipsing binary Zeta Phoenicis. The system's orbital period of 1.6697739 days implies a GW frequency of 13.863 $mu$Hz, a regime inaccessible to conventional interferometric detectors. Using 20 years of hourly pressure data from more than 100 stations, we apply a communicationsu2011engineering approach combining coherent integration, superheterodyne frequency shifting, and iterative phaseu2011demodulation to isolate weak, structured oscillations. After compensating for frequency drift and multiple phase modulations, we recover a narrow, persistent spectral feature at the predicted frequency. One modulation matches the annual Doppler signature expected from Earth’s orbital motion, while additional lowu2011frequency sidebands may reflect longeru2011period dynamical influences within the source system. We further derive a longu2011term decrease in the GW frequency, corresponding to a secular increase in the orbital period, and provide a prediction for the period in 2026. These results demonstrate that phaseu2011sensitive demodulation techniques can extract ultrau2011lowu2011frequency, coherent signals from noisy geophysical data and may offer a complementary pathway for probing continuous GW sources in the microhertz regime.