A new prime factor FFT algorithm and its index mapping

There are many different FFT algorithms, most of which can be distinguished coarsely as common factor algorithm (CFA) and prime factor algorithm (PFA) by the scheme of decomposing two input sequences. Some relationship between CFA and PFA is established by combining the schemes of decomposing data sequences called index mapping schemes for CFA and PFA together. The relationship established shows that PFA can be implemented non in place in order, in place non in order, non in place non in order, or in place in order with no requirement for unscrambling data sequences. The new PFA algorithms have different structures from that of conventional ones. With the new algorithm a batch of data of the original input sequence for computation of each small point FFT is drawn directly and orderly and then a rotating operator modulo N₁ or modulo N₂ rather than modulo N₁N₂ as conventional PFA is imposed on the batch of data and about 50% integer arithmetic operation for address generation is reduced. The new PFA algorithm do not need Chinese remainder theorem as a tool of index mapping