In this paper, a super-resolution method based on the Discrete Cosine Transform (DCT) is proposed for a signal with some frequency damage. If the damage process can be modeled as linear convolutoin with a type 1 linear phase FIR filter, it is shown that some DCT coefficients of the damaged signal are the same as those of the original signal except for the DCT coefficients corresponding to the frequency damage. From this investigation, the proposed method is provided for the DCTs with four types as expanding the super-resolution method based on the Discrete Fourier Transform (DFT). In addition,two magnification approaches based on the proposed method are described to improve the conventional approach.