Cyclic filter banks are appropriate for processing finite-length signals such as images since cyclic convolutions are used to process them. So far, it has been shown that the two channel linear phase orthogonal filter banks, which can not be realized as non-cyclic LTI systems, can be realized as cyclic LTI systems. This paper proposes a design of the cyclic filter banks with DFT modulations. First, we show the polyphase representations and perfect reconstruction conditions. Next, we discuss the advantages of the proposed structure by studying the essential property of the cyclic LTI systems. Finally, we give a design example of the proposed filter banks, and show the reconstructed images processed by the proposed filter banks.