•A new sparse signal representation in the frequency domain is presented for target recognition in SAR image.•A frequency prescreening skill is developed to generate representation in the transformed domain.•The recognition performance of proposed method is verified in several unconstrained scenarios, including the change of pose, configuration, and depression angle, spatial translation, articulation and occlusion. Classical sparse modeling requires accurate alignment between the query and the training data. This precondition is disadvantageous for target recognition tasks, where, although the target is present in the images, it is infeasible to perfectly register it during training. In addition, the classical approach is less powerful under unconstrained operating conditions. To solve these problems, this paper presents a new sparse signal modeling strategy in the frequency domain. Because signal energy is mainly concentrated on a small portion of low-frequency components, this set of spectrum carries vital information that can be used to discriminates the class of a target. We generated representations by aggregating low-frequency components. They were then used to build sparse signal models. More specifically, the spectral representation of training data were concatenated to form an over-complete dictionary to encode the counterpart of the query as a linear combination of themselves. Sparsity was harnessed to generate an optimal solution, from which an inference can be made. Multiple comparative analyses were made to demonstrate the advantages of the proposed strategy, especially in unconstrained environments.