Abstract: Four types of the DFT(DFT-j,j=Ⅰ, Ⅱ, Ⅲ, Ⅳ)are introduced in this paper.The relationship among four types of the DFT and their inherent properties are explored. Anew real-multiplier FFT algorithm is proposed for all four types of the N=2^m DFT. First,thealgorithm formulae represented by Kronecker product and direct sum are derived. Then,thesignal flowgraph for the length-23 FFT is given to illustrate the proposed algorithm. Finally,the computational complexity is analysed and a comparison is made with traditional radix-2algorithm and other existing real-multiplier FFT algorithms. The proposed algorithmrequires the minimum number of arithmetic operations and uses real multipliers and allowsin-place computation. The simple and regular structure makes it easy to be implemented.