Input and/or Output Pruning of Composite Length FFTs Using a DIF-DIT Transform Decomposition

Unified commutation-pruning technique for efficient computation of composite DFTs

“…Sorensen et al, in [23], proposed two methods to prune composite length DFTs, first one to prune the input and another one to prune the output. Next, the methodology of Medina-Melendrez et al, in [24], merges the methods developed originally in [23] to obtain a composite structure that is capable to prune the input and/or output of a general decomposed transform at the same time. It was demonstrated, in [24], that such a computational structure could be as efficient as the one based on specific FFT algorithms [15][16][17].…”

“…Next, the methodology of Medina-Melendrez et al, in [24], merges the methods developed originally in [23] to obtain a composite structure that is capable to prune the input and/or output of a general decomposed transform at the same time. It was demonstrated, in [24], that such a computational structure could be as efficient as the one based on specific FFT algorithms [15][16][17]. In [24], a new methodology for decomposition over a composite length DFT has been proposed as a modification of the Sorensen's approach [23].…”

“…It was demonstrated, in [24], that such a computational structure could be as efficient as the one based on specific FFT algorithms [15][16][17]. In [24], a new methodology for decomposition over a composite length DFT has been proposed as a modification of the Sorensen's approach [23]. Furthermore, the [24] suggests, first, to perform decimation in frequency (DIF) and, second, a decimation in time (DIT).…”

“…In [24], a new methodology for decomposition over a composite length DFT has been proposed as a modification of the Sorensen's approach [23]. Furthermore, the [24] suggests, first, to perform decimation in frequency (DIF) and, second, a decimation in time (DIT). For processing of spatial data, the corresponding decimation in the space domain should be performed similarly to the DIT operation for time data processing.…”

“…The decomposed transform is then pruned by eliminating, from the input and output stages, additions and multiplications by zero, multiplications by one, and all other computations not needed to obtain the required Fourier transform coefficients. In [24], such the multistage decomposed and pruned transform is referred to as FFT DIF−DIT−TD (here, that method is referred as DFT DIF−DIT−Pr ). Nevertheless, both methods addressed in [23,24] do not achieve the lowest attainable number of the required arithmetic operations.…”