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A comparative review of real and complex Fourier-related transforms

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1 Author(s)
Ersoy, O.K. ; Sch. of Electr. Eng., Purdue Univ., West Lafayette, IN, USA

Major continuous-time, discrete-time, and discrete Fourier-related transforms as well as Fourier-related series are discussed both with real and complex kernels. The complex Fourier transforms, Fourier series, cosine, sine, Hartley, Mellin, Laplace transforms, and z-transforms are covered on a comparative basis. Generalizations of the Fourier transform kernel lead to a number of novel transforms, in particular, special discrete cosine, discrete sine, and real discrete Fourier transforms, which have already found use in a number of applications. The fast algorithms for the real discrete Fourier transform provide a unified approach for the optimal fast computation of all discrete Fourier-related transforms. The short-time Fourier-related transforms are discussed for applications involving nonstationary signals. The one-dimensional transforms discussed are also extended to the two-dimensional transforms

Published in:

Proceedings of the IEEE  (Volume:82 ,  Issue: 3 )