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The Hilbert-Huang transform (HHT) is a relatively new time-frequency analysis tool. We present a new signal feature extraction technique based on HHT. This technique is used to extract diurnal and semidiurnal tides from atmospheric pressure data obtained from a microbarograph stationed at the Arecibo Observatory. Observation of seasonal variations of semidiurnal tides is possible due to the high precision offered by this technique. Furthermore, we apply the signal extraction procedure to isolate and remove high-amplitude disturbance signals from the time-series signal. This is demonstrated by extracting a hurricane event from the pressure data. The superior capabilities of the HHT-based technique to analyze time-varying signals compared to traditional linear techniques such as the wavelet transform and the fast Fourier transform are demonstrated.