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Based on the coupling relationship among radial velocity, range walk, and Doppler frequency of the moving target's echoes, a novel method is proposed, i.e., Radon-Fourier transform (RFT), to realize the long-time coherent integration for radar target detection. The RFT realizes the echoes spatial-temporal decoupling via joint searching along range and velocity directions, as well as the successive coherent integration via the Doppler filter bank. Besides, four equivalent RFTs are obtained with respect to the different searching parameters. Furthermore, a generalized form of RFT, i.e., generalized Radon-Fourier transform (GRFT), is also defined for target detection with arbitrary parameterized motion. Due to the similarity between the RFT and the well-known moving target detection (MTD) method, this paper provides detailed comparisons between them on five aspects, i.e., coherent integration time, filter bank structure, blind speed response, detection performance, and computational complexity. It is shown that MTD is actually a special case of RFT and RFT is a kind of generalized Doppler filter bank processing for targets with across range unit (ARU) range walk. Finally, numerical experiments are provided to demonstrate the equivalence among four kinds of RFTs. Also, it is shown that the RFT may obtain the coherent integration gain in the different noisy background and the target's blind speed effect may be effectively suppressed. In the meantime, both the weak target detection performance and the radar coverage of high-speed targets may be significantly improved via RFT without change of the radar hardware system.