FAST COMPUTATION OF REAL DISCRETE FOURIER-TRANSFORM FOR ANY NUMBER OF DATA POINTS

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. Then, this is generalized to any number of factors with arbitrary radices. Each factor M involves the computation of size M RDFT which is carried out by the best size-M RFFT algorithm available. The RFFT algorithm for M equal to 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.