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Non-uniform discrete Fourier transform
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Non-uniform discrete Fourier transform : ウィキペディア英語版
Non-uniform discrete Fourier transform
In applied mathematics, the non-uniform discrete Fourier transform (NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier transform, but in which the input signal is not sampled at equally spaced intervals. As a result of this, the computed Discrete Fourier Transform can also consist of unevenly sampled frequency values. It is however also possible to compute uniformly sampled frequency values from an unevenly sampled input signal.
As a generalized approach for nonuniform sampling, NDFT can help us to get the information of a finite length signal in frequency domain at any frequency. It can also be used to design the FIR filters as the role of DFT, no matter if it's 1-D or 2-D.
One of the reasons to adopt NDFT is that most signals have their energy distributed nonuniformly in the frequency domain. Therefore, a nonuniform sampling scheme could be more convenient and useful in lots of applications of Digital Signal Processing (DSP). For example, NDFT provides a variable spectral resolution controlled by the users.
Note that NDFT reduces to DFT when the sampling points are located on the unit circle at equally spaced angles.
==1-D NDFT==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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