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Properties of the Multidimensional Generalized Discrete Fourier Transform
November 1979 (vol. 28 no. 11)
pp. 819-830
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.
Index Terms:
signal processing, Fast algorithms, fast Fourier transform, generalized discrete Fourier transform, multidimensional processing
Citation:
P. Corsini, G. Frosini, "Properties of the Multidimensional Generalized Discrete Fourier Transform," IEEE Transactions on Computers, vol. 28, no. 11, pp. 819-830, Nov. 1979, doi:10.1109/TC.1979.1675262
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