Research on algorithm and implementation of Fourier transform in the case of N < M

In this paper, Fourier transform (FT) is studied under a special situation in which the transform length N is less than the number of input data M. First, the corresponding Fourier transform formula is deduced, and then an implementation example is given as well as performance simulation and implementation analysis. The results show that the mixed radix FT method has less resource consumption and less processing latency compared with fast Fourier transform (FFT) and discrete Fourier transform (DFT) method, respectively. The proposed N < M FT method increases the flexibility of traditional Fourier transform algorithm.