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The wireless signal propagates via multipath arising from different reflections and penetration between a transmitter and receiver. Extracting multipath profiles (e.g., delay and Doppler along each path) from received signals enables many important applications, such as channel prediction and crossband channel estimation (i.e., estimating the channel on a different frequency). The benefit of multipath estimation further increases with mobility since the channel in that case is less stable and more important to track. Yet high-speed mobility poses significant challenges to multipath estimation. In this paper, instead of using time-frequency domain channel representation, we leverage the delay-Doppler domain representation to accurately extract and predict multipath properties. Specifically, we use impulses in the delay-Doppler domain as pilots to estimate the multipath parameters and apply the multipath information to predicting wireless channels as an example application. Our design rationale is that mobility is more predictable than the wireless channel since mobility has inertial while the wireless channel is the outcome of a complicated interaction between mobility, multipath, and noise. We evaluate our approach via both acoustic and RF experiments, including vehicular experiments using USRP. Our results show that the estimated multipath matches the ground truth, and the resulting channel prediction is more accurate than the traditional channel prediction schemes.