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A family of Discrete Fourier Transforms with Pseudo-Cyclic Convolution Properties

M. Unser

Proceedings of the Twelfth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'87), Dallas TX, USA, April 6-9, 1987, vol. III, pp. 1815-1818.



An extended family of discrete Fourier transforms is introduced. These transforms, which may be implemented by using FFTs, allow the computation of pseudocyclic convolutions by multiplication in the transform domain. The choice of a suitable transform (DFT1/4) or the combined use of two complementary transforms allows a fast and efficient computation of aperiodic convolutions of waveforms of duration N by using N-point transforms that require no zero padding. Finally, all members of this family are shown to be equivalent asymptotically to the Karhunen-Loève transform of an arbitrary wide sense stationary process.


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