Open AccessResearch on algorithm and implementation of Fourier transform in the case of N < M
Author(s) -
Yang Gao,
Jia Li Zhu,
Yun Fei Li,
Jian Liu
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1634/1/012067
Subject(s) - discrete fourier transform (general) , fractional fourier transform , fourier transform , prime factor fft algorithm , fast fourier transform , non uniform discrete fourier transform , cyclotomic fast fourier transform , hartley transform , algorithm , split radix fft algorithm , discrete time fourier transform , harmonic wavelet transform , cooley–tukey fft algorithm , short time fourier transform , discrete hartley transform , computer science , mathematics , arithmetic , fourier analysis , mathematical analysis , artificial intelligence , discrete wavelet transform , wavelet transform , wavelet
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.