Nonstationary time series are ubiquitous in almost all natural and engineering systems. Capturing the time-varying signatures from nonstationary time series is still a challenging problem for data mining. Quadratic Time-Frequency Distribution (TFD) provides a powerful tool to analyze these data. However, they suffer from Cross-Term (CT) issues that impair the readability of TFDs. Therefore, to achieve high-resolution and CT-free TFDs, an end-to-end architecture termed Quadratic TF-Net (QTFN) is proposed in this paper. Guided by classic TFD theory, the design of this deep learning architecture is heuristic, which firstly generates various basis functions through data-driven. Thus, more comprehensive TF features can be extracted by these basis functions. Then, to balance the results of various basis functions adaptively, the Efficient Channel Attention (ECA) block is also embedded into QTFN. Moreover, a new structure called Muti-scale Residual Encoder-Decoder (MRED) is also proposed to improve the learning ability of the model by highly integrating the multi-scale learning and encoder-decoder architecture. Finally, although the model is only trained by synthetic signals, both synthetic and real-world signals are tested to validate the generalization capability and superiority of the proposed QTFN.