Time−frequency analysis (TFA) is regarded as an efficient technique to reveal the hidden characteristics of the oscillatory signal. At present, the traditional TFA methods always construct the signal model in the time domain and assume the instantaneous features of the modes to be continuous. Thus, most of these approaches fail to tackle some specific kinds of impulselike signal, including shock and vibration waves, damped tones, or marine mammals. This article introduces a new method called generalized horizontal synchrosqueezing transform (GHST) to process the transient signal. A signal model defined in the frequency domain is used to deduce the GHST. Next, the new synchrosqueezing operator termed as group delay (GD) is proposed based on high-order Taylor expansions of the signal model. Finally, the modulus around ridge curves is rearranged from the original position to the estimated GD. Numerical results of a simulated signal demonstrate the precision of the GHST in terms of both readability of the time−frequency representation and reconstruction accuracy. Additionally, the proposed method is implemented to diagnose the fault in a rotary machine by analyzing the vibration signal. The validation demonstrates that the GHST performs better than other traditional TFA methods, and it is qualified for the online condition monitoring of the industrial mechanical system.