Since the response of a spindle with sudden unbalance shows non-stationary characteristics, it cannot be extracted by signal processing methods using traditional Fourier transform. To tackle this problem, a new signal extracting method combining wavelet de-noising technique and the short time Fourier transform method is proposed in this paper. Firstly, the non-stationary signal of the spindle is filtered and reconstructed by the wavelet de-noising technique. Then, the amplitude of the unbalance response is acquired by the short time Fourier transform method. Finally, the feasibility and the accurately of the proposed method is verified by numerical simulation and practical experiment.