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Extended Fourier analysis of signals. (arXiv:1303.2033v8 [cs.DS] UPDATED)
来源于:arXiv
This summary of the doctoral thesis is created to emphasize the close
connection of the proposed spectral analysis method with the Discrete Fourier
Transform (DFT), the most extensively studied and frequently used approach in
the history of signal processing. It is shown that in a typical application
case, where uniform data readings are transformed to the same number of
uniformly spaced frequencies, the results of the classical DFT and proposed
approach coincide. The difference in performance appears when the length of the
DFT is selected to be greater than the length of the data. The DFT solves the
unknown data problem by padding readings with zeros up to the length of the
DFT, while the proposed Extended DFT (EDFT) deals with this situation in a
different way, it uses the Fourier integral transform as a target and optimizes
the transform basis in the extended frequency range without putting such
restrictions on the time domain. Consequently, the Inverse DFT (IDFT) applied
to the res 查看全文>>