Due to sophisticated deployments of all kinds of wireless networks (e.g., 5G, Wi-Fi, Bluetooth, LEO satellite, etc.), multiband signals distribute in a large bandwidth (e.g., from 70 MHz to 8 GHz). Consequently, for network monitoring and spectrum sharing applications, a sniffer for extracting physical layer information, such as structure of packet, with low sampling rate (especially, sub-Nyquist sampling) can significantly improve their cost- and energy-efficiency. However, to achieve a multiband signals sniffer is really a challenge. To this end, we propose Sums, a system that can sniff and analyze multiband signals in a blind manner. Our Sums takes advantage of hardware and algorithm co-design, multi-coset sub-Nyquist sampling hardware, and a multi-task deep learning framework. The hardware component breaks the Nyquist rule to sample GHz bandwidth, but only pays for a 50 MSPS sampling rate. Our multi-task learning framework directly tackles the sampling data to perform spectrum sensing, physical layer protocol recognition, and demodulation for deep inspection from multiband signals. Extensive experiments demonstrate that Sums achieves higher accuracy than the state-of-the-art baselines in spectrum sensing, modulation classification, and demodulation. As a result, our Sums can help researchers and end-users to diagnose or troubleshoot their problems of wireless infrastructures deployments in practice.