To ensure the durability and safety of electric vehicles (EVs), it is vital to monitor the capacity deterioration of lithium-ion batteries (LIBs). However, due to complex physicochemical interactions and temperature effects, the capacity of LIBs cannot be directly measured. This work presents a novel generalized approach for estimating the capacity of LIBs based on the adaptive empirical wavelet transform (EWT) and long-short-term memory neural network (LSTM). The adaptive EWT is a potent tool for analyzing the charging-discharging terminal voltage signal with non-stationary and transient phenomena of the LIBs in the time-frequency domain. Specifically, the measured voltage signals of the LIBs are decomposed into nine multi-resolution modes to display the high and low-frequency components. Then, 13 statistical features are extracted to investigate the correlation between the capacity degradation and the extracted features. Afterwards, the LSTM model is developed to estimate the capacity of the LIBs. The proposed approach has been validated using two datasets: (1) NASA's randomized dataset with 24 LIBs cycled under generally varying operational conditions and (2) Stanford University's dataset with 10 LIBs cycled with EV discharge current profile. Compared with the state-of-the-art, the proposed method accurately estimates LIB capacity with an average root mean square error of 1.26 % and a maximum error of 2.74 %.