In response to the issues of high sampling rate and large reconstruction computation for Ultra-Wideband LFM signal in existing MWC systems, a novel MWC sampling structure based on overlapping windows is proposed, which can turn a wideband LFM into multiple small bandwidth signals with frequency sparsity. In the designing of overlapping window, the symmetry of LFM’s time-frequency windowing is utilized for suppressing energy leakage and ensuring the sparsity in the frequency domain. This structure overcomes the traditional limitations on sampling rate and does not require prior knowledge of the chirp rate. Simulations and tests on real-world signals confirm the effectiveness of the proposed structure for LFM signal processing. Experimental results show that this approach not only reduces the required sampling rate but also enables efficient and stable signal reconstruction under various SNR conditions. Compared to traditional compressed sampling and rectangular window segmentation methods, the proposed structure demonstrates significant advantages in both reconstruction accuracy and sampling efficiency.