A fast Fourier transform algorithm for computing N=N(1)xN(2)-point DFT, where both factors N-1 and N-2 are smaller positive integer, said to be a double factors algorithm(DFA), is developed. The DFA subdivides a DFT o...
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ISBN:
(纸本)9781424439867
A fast Fourier transform algorithm for computing N=N(1)xN(2)-point DFT, where both factors N-1 and N-2 are smaller positive integer, said to be a double factors algorithm(DFA), is developed. The DFA subdivides a DFT of length N=N(1)xN(2) into smaller transforms of length N-1 and N-2 and takes the following steps:(1) computes N1N2-point DFTs, (2) multiplies the values of DFT by twiddle factors, (3) computes N2N1-point DFTs. The structure of the DFA is similar to those of the most simple PFA and WFTA, but N-1 and N-2 are not necessarily relatively prime. When N=2(M) or 4(M), the total number of computations of DFT in the DFA is less than those in the radix-2 and radix-4 FFT algorithm but slightly more than that in the split-radix FFT algorithm. When N is other values, the total number of computations of DFT in the DFA is less than those in the PFA and WFTA.
A fast Fourier transform algorithm for computing N=N_1×N_2-point DFT, where both factors N_1 and N_2 are smaller positive integer, said to be a double factors algorithm (DFA), is developed. The DFA subdivides a D...
详细信息
ISBN:
(纸本)9781424439874
A fast Fourier transform algorithm for computing N=N_1×N_2-point DFT, where both factors N_1 and N_2 are smaller positive integer, said to be a double factors algorithm (DFA), is developed. The DFA subdivides a DFT of length N=N_1×N_2 into smaller transforms of length N_1 and N_2 and takes the following steps:(1) computes N_1 N_2-point DFTs, (2) multiplies the values of DFT by twiddle factors, (3) computes N_2 N_1-point DFTs. The structure of the DFA is similar to those of the most simple PFA and WFTA, but N_1 and N_2 are not necessarily relatively prime. When N=2~M or 4~M, the total number of computations of DFT in the DFA is less than those in the radix-2 and radix-4 FFT algorithm but slightly more than that in the split-radix FFT algorithm. When N is other values, the total number of computations of DFT in the DFA is less than those in the PFA and WFTA.
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