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Fast computation of real discrete Fourier transform for any number of data points

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2 Author(s)
Hu, N.-C. ; Nat. Taiwan Inst. of Technol., Taipei, Taiwan ; Ersoy, O.K.

In many applications, it is desirable to have a fast algorithm (RFFT) for the computation of the real discrete Fourier transform (RDFT) for any number of data points N. To achieve this, the two-factor Cooley-Tukey decimation-in-time and decimation-in-frequency RFFT algorithms are first developed and expressed in terms of matrix factorization using Kronecker products. This is generalized to any number of factors with arbitrary radices. Each factor M involves the computation of the size-M RDFT, which is carried out by the best size-M RFFT algorithm available. The RFFT algorithm for the case where M is a prime number is also developed. The RFFT algorithms are more efficient in the number of operations when the factors are arranged in a certain order, unlike the Cooley-Tukey complex FFT algorithms. which have the same number of operations for any order of the factors

Published in:

Circuits and Systems, IEEE Transactions on  (Volume:38 ,  Issue: 11 )

Date of Publication:

Nov 1991

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