Vector radix fast Fourier transform

Vector coding algorithms for multidimensional discrete Fourier transform

“…It should be pointed out that a variety of different algorithms for the multidimensional DFT have been developed, for instance: the vector-radix algorithms, the polynomial transform (PT) algorithms, the nested algorithms, the split vector-radix (SVR) algorithms and so forth [8,13,12,2]. These algorithms can reduce the arithmetic complexity more significantly than the RC algorithm.…”

Discrete fourier transform on multicore

“…Both (17) and (18) are derived from (15) using (9) and (10). The required matrix transposition can be blocked using (11) and (12) for more efficient data movement.…”

Evaluation of two-dimensional discrete Fourier transforms via generalized FFT algorithms

“…A 2-D sequence i(n1,n2) is periodic if it has the property + ) = (a) (1) for all integer vectors n and r and some 212 integer mstrix N with a nonzero determinant. A 2-D periodic sequence repeats itself in the directions defined by the vectors forming the columns of the periodicity matrix N. If N is diagonal, the sequence it describes is said to be rectangularly periodic.…”

“…These transforms are generally computed either as a series of l-D DFT'a obtained from a row-column decomposition of the DFT sum or as a series of smaller 2-D DFT's via the vector-radix algorithm (1).…”