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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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Proceedings ArticleDOI
17 Oct 2015
TL;DR: In this paper, the authors presented an algorithm for robustly computing sparse Fourier transforms in the continuous setting, with sample complexity linear in k and logarithmic in the signal-to-noise ratio and the frequency resolution.
Abstract: In recent years, a number of works have studied methods for computing the Fourier transform in sub linear time if the output is sparse. Most of these have focused on the discrete setting, even though in many applications the input signal is continuous and naive discretization significantly worsens the sparsity level. We present an algorithm for robustly computing sparse Fourier transforms in the continuous setting. Let x(t) = x*(t) + g(t), where x* has a k-sparse Fourier transform and g is an arbitrary noise term. Given sample access to x(t) for some duration T, we show how to find a k-Fourier-sparse reconstruction x'(t) with [frac{1}{T}int0T abs{x(t) - x(t)}2 mathrm{d} t lesssim frac{1}{T}int0T abs{g(t)}2 mathrm{d}t. The sample complexity is linear in k and logarithmic in the signal-to-noise ratio and the frequency resolution. Previous results with similar sample complexities could not tolerate an infinitesimal amount of i.i.d. Gaussian noise, and even algorithms with higher sample complexities increased the noise by a polynomial factor. We also give new results for how precisely the individual frequencies of x* can be recovered.

37 citations

Journal ArticleDOI
TL;DR: A new source for the multiplicity of the weight-type fractional Fourier transform (WFRFT) is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters, which provides a unified framework for the FRFT.
Abstract: The fractional Fourier transform (FRFT) has multiplicity, which is intrinsic in fractional operator. A new source for the multiplicity of the weight-type fractional Fourier transform (WFRFT) is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters $$ \mathfrak{M},\mathfrak{N} \in \mathbb{Z}^M $$ . Therefore a generalized fractional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform (MPFRFT). It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.

37 citations

Journal ArticleDOI
TL;DR: For a regular twistor D-module and for a given function f, the authors compare the nearby cycles at f = ∞ and the nearby or vanishing cycles at τ = 0 for its partial Fourier-Laplace transform relative to the kernel e−τf.
Abstract: For a regular twistor D-module and for a given function f , we compare the nearby cycles at f = ∞ and the nearby or vanishing cycles at τ = 0 for its partial Fourier-Laplace transform relative to the kernel e−τf .

36 citations

Patent
01 Oct 1973
TL;DR: In this paper, a discrete frequency domain equalization system was proposed for high-speed synchronous data transmission systems, where, in a preferred embodiment, samples of an input signal in the time domain are transformed by a discrete fast Fourier transform device into samples in the frequency domain.
Abstract: A discrete frequency domain equalization system is disclosed for utilization in a high-speed synchronous data transmission system where, in a preferred embodiment, samples of an input signal in the time domain are transformed by a discrete fast Fourier transform device into samples in the frequency domain. Reciprocal values of these frequency domain samples are derived from a reciprocal circuit and then transformed by an inverse discrete fast Fourier transform device into time domain samples which are the desired tap gains that are applied to a transversal equalizer in order to minimize the errors in a received signal caused by intersymbol interference and noise.

36 citations

Journal ArticleDOI
Pierre Duhamel1, B. Piron1, J.M. Etcheto1
TL;DR: The authors indicate an apparently novel method for computing an inverse discrete Fourier transform (IDFT) through the use of a forward DFT program, and point out that, in many cases, this is obtained without any additional cost, either in terms of program length or in Terms of computational time.
Abstract: The authors indicate an apparently novel method for computing an inverse discrete Fourier transform (IDFT) through the use of a forward DFT program. They point out that, in many cases, this is obtained without any additional cost, either in terms of program length or in terms of computational time. >

36 citations


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