Istituto di Scienza e Tecnologie dell'Informazione     
Corsini P., Frosini G. Properties of the multidimensional generalized discrete fourier transform. In: Ieee Transactions on Computers, vol. 28 (11) pp. 819 - 830. 1979.
In this work the generalized discrete Fourier transform (GFT), which includes the DFT as a particular case, is considered. Two pairs of fast algorithms for evaluating a multidimensional GFT are given (T-algorithm, F-algorithm, and T'- algorithm, F'-algorithm). It is shown that in the case of the DFT of a vector, the T-algorithm represents a form of the classical FFT algorithm based on a decimation in time, and the F-algorithm represents a form of the classical FFT algorithm based on decimation in frequency. Moreover, it is shown that the T'-algorithm and the T-algorithm involve exactly the same arithmetic operations on the same data. The same property holds for the F'-algorithm and the F-algorithm. The relevance of such algorithms is discussed, and it is shown that the T'-algorithms and the F'-algorithm are particularly advantageous for evaluating the DFT of large sets of data.
Subject Fast algorithms
fast Fourier transform
generalised discrete Fourier transform
multidimensional processing
signal processing

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