Issue No. 11 - November (1979 vol. 28)
P. Corsini , Dipartimento Sperimentale di Elettrotecnica ed Elettronica, Facolta di Ingegneria, Universit? di Pisa
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'-algorithm and the F'-algorithm are particularly advantageous for evaluating the DFT of large sets of data.
signal processing, Fast algorithms, fast Fourier transform, generalized discrete Fourier transform, multidimensional processing
P. Corsini, G. Frosini, "Properties of the Multidimensional Generalized Discrete Fourier Transform", IEEE Transactions on Computers, vol. 28, no. , pp. 819-830, November 1979, doi:10.1109/TC.1979.1675262