Existing research on multi-component radar signal recognition widely adopts recognition frameworks based on time-frequency transformation (TFT) and convolutional neural networks (CNN). To address the issue of the vulnerability of traditional TFT-generated time-frequency representations (TFR) to noise under low signal-to-noise ratio (SNR) conditions, we propose a new TFT scheme, called Multi-Scale TFT Network (MTFT-Net). Specifically, MTFT-Net learns diverse and comprehensive basis functions to obtain various TF features of time-domain multi-component radar signals. It then uses subsequent aggregation modules to concentrate and reconstruct the energy of the TF features, ultimately outputting the TFR. Experimental results show that MTFT-Net generates better TFRs with superior noise resistance under low SNR conditions compared to traditional TFT methods. Moreover, MTFT-Net can mimic the styles of various traditional TFTs. Finally, we compare its performance with the advanced TFA-Net to demonstrate the effectiveness of the proposed method.