Oscillatory phenomena abound in many types of signals. Identifying the individual oscillatory components that constitute an observed biological signal leads to profound understanding about the biological system. The instantaneous frequency (IF), the amplitude modulation (AM), and their temporal variability are widely used to describe these oscillatory phenomena. In addition, the shape of the oscillatory pattern, repeated in time for an oscillatory component, is also an important characteristic that can be parametrized appropriately. These parameters can be viewed as phenomenological surrogates for the hidden dynamics of the biological system. To estimate jointly the IF, AM, and shape, this paper applies a novel and robust time-frequency analysis tool, referred to as the synchrosqueezing transform (SST). The usefulness of the model and SST are shown directly in predicting the clinical outcome of ventilator weaning. Compared with traditional respiration parameters, the breath-to-breath variability has been reported to be a better predictor of the outcome of the weaning procedure. So far, however, all these indices normally require at least 20 min of data acquisition to ensure predictive power. Moreover, the robustness of these indices to the inevitable noise is rarely discussed. We find that based on the proposed model, SST and only 3 min of respiration data, the ROC area under curve of the prediction accuracy is 0.76. The high predictive power that is achieved in the weaning problem, despite a shorter evaluation period, and the stability to noise suggest that other similar kinds of signal may likewise benefit from the proposed model and SST.