Abstract: In congested spectral environments, transmitting signals in several discontinuous frequency segments and coherent synthesizing at the receiver side is a method for obtaining signals with large equivalent bandwidth. This paper investigates the discontinuous spectrum-frequency modulated continuous wave (DS-FMCW) and its application in high frequency radar specially. Firstly, a sampling point displacement method is proposed, and a spectral analysis model of non-uniformly sampled sequences for the fast-time processing of DS-FMCW is established. Secondly, two-dimensional range-Doppler spectral estimation model is developed, and processing schemes for handling range migration are proposed for DS-FMCW. Finally, to solve the problem of high range sidelobes, range and range-Doppler spectral estimation methods for DS-FMCW are proposed based on an iterative sparse recovery algorithm which is applicable in the single-snapshot scenario. Fast implementations of these spectral estimation methods are also presented. Simulation experiments show that the proposed range-Doppler processing schemes of DS-FMCW are able to compensate the range migration effectively, and when the utilization rate of the frequency band is above 20%, the proposed spectral estimation method can steadily resolve two targets which are separated by one third of the intrinsic radar range resolution in the range domain, and its range estimation accuracy is better than the classical least-squares algorithm and the orthogonal matching pursuit algorithm. Finally, the proposed fast implementation algorithm is verified to have a low computational complexity in a single iteration, which makes it suitable for real-time systems.