The new real-multiplier FFT-j algorithms

In this paper four different versions of the DFT (DFT-j,j=I,II,III,IV) are first introduced, Then, the relationship among four different versions of the DFT and their inherent properties are explored. The new real-multiplier FFT-j algorithms are proposed for all four versions of the N=2^m DFT. The algorithm formulae are derived, represented by Kronecker product and direct sum. Finally, the signal flowgraph for the length-2³ FFT-j is given to illustrate the proposed algorithms. The computational complexity is analysed and a comparison is made with other existing real-multiplier FFT algorithms. The proposed algorithms require the minimum number of arithmetic operations and use real multipliers and allow in-place computation. Besides, the proposed algorithms have very simple and regular structure. They have been implemented by software and have been finding practical applications