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Non-uniform discrete Fourier transform

About: Non-uniform discrete Fourier transform is a research topic. Over the lifetime, 4067 publications have been published within this topic receiving 123952 citations.


Papers
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Journal ArticleDOI
TL;DR: This work applies the language of the unified FT to develop FRT expressions for discrete and continuous signals, introducing a particular form of periodicity: chirp-periodicity.
Abstract: The fractional Fourier transform (FRT) is an extension of the ordinary Fourier transform (FT). Applying the language of the unified FT, we develop FRT expressions for discrete and continuous signals, introducing a particular form of periodicity: chirp-periodicity. The FRT sampling theorem is derived as an extension of its ordinary counterpart.

152 citations

Book ChapterDOI
TL;DR: The fractional Fourier transform (FFT) as discussed by the authors is a generalization of the ordinary FFT with an order parameter a, and it is used to interpolate between a function f(u) and its FFT F(μ).
Abstract: Publisher Summary This chapter is an introduction to the fractional Fourier transform and its applications. The fractional Fourier transform is a generalization of the ordinary Fourier transform with an order parameter a . Mathematically, the a th order fractional Fourier transform is the a th power of the Fourier transform operator. The a = 1st order fractional transform is the ordinary Fourier transform. In essence, the a th order fractional Fourier transform interpolates between a function f(u) and its Fourier transform F(μ) . The 0th order transform is simply the function itself, whereas the 1st order transform is its Fourier transform. The 0.5th transform is something in between, such that the same operation that takes us from the original function to its 0.5 th transform will take us from its 0.5th transform to its ordinary Fourier transform. More generally, index additivity is satisfied: The a 2 th transform of the a 1 th transform is equal to the ( a 2 + a 1 )th transform. The –1th transform is the inverse Fourier transform, and the – a th transform is the inverse of the a th transform.

151 citations

Journal ArticleDOI
TL;DR: In this paper, the influence of time-domain noise on the results of a discrete Fourier transform (DFT) was studied and it was shown that the resulting frequency domain noise can be modeled using a Gaussian distribution with a covariance matrix which is nearly diagonal.
Abstract: An analysis is made to study the influence of time-domain noise on the results of a discrete Fourier transform (DFT). It is proven that the resulting frequency-domain noise can be modeled using a Gaussian distribution with a covariance matrix which is nearly diagonal, imposing very weak assumptions on the noise in the time domain.

150 citations

Journal ArticleDOI
TL;DR: In this article, the Laplace transform of the solution for TEM soundings over an N-layer earth was derived and used to invert it numerically using the Gaver-Stehfest algorithm.
Abstract: Calculations for the transient electromagnetic (TEM) method are commonly performed by using a discrete Fourier transform method to invert the appropriate transform of the solution. We derive the Laplace transform of the solution for TEM soundings over an N-layer earth and show how to use the Gaver-Stehfest algorithm to invert it numerically. This is considerably more stable and computationally efficient than inversion using the discrete Fourier transform.

149 citations

Journal ArticleDOI
TL;DR: The Synchrosqueezing Transform (SST) as discussed by the authors is an extension of the wavelet transform incorporating elements of empirical mode decomposition and frequency reassignment techniques, which produces a well defined time-frequency representation allowing the identification of instantaneous frequencies in seismic signals.
Abstract: Time-frequency representation of seismic signals provides a source of information that is usually hidden in the Fourier spectrum. The short-time Fourier transform and the wavelet transform are the principal approaches to simultaneously decompose a signal into time and frequency components. Known limitations, such as trade-offs between time and frequency resolution, may be overcome by alternative techniques that extract instantaneous modal components. Empirical mode decomposition aims to decompose a signal into components that are well separated in the time-frequency plane allowing the reconstruction of these components. On the other hand, a recently proposed method called the “synchrosqueezing transform” (SST) is an extension of the wavelet transform incorporating elements of empirical mode decomposition and frequency reassignment techniques. This new tool produces a well-defined time-frequency representation allowing the identification of instantaneous frequencies in seismic signals to highlight ...

148 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202318
202233
20213
20201
20191
20189