Topic
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 published on a yearly basis
Papers
More filters
TL;DR: In this article, the authors proposed a quasicrystals-based irregular sampling strategy to reduce the number of measures needed to recover a signal or an image whose Fourier transform is supported by a compact set with a given measure.
Abstract: This contribution is addressing an issue named in signal processing. Let be a lattice and be the dual lattice. Then the standard Shannon–Nyquist theorem says that any signal f whose Fourier transform is supported by a compact subset can be recovered from the samples if and only if the translated sets are pairwise disjoint. This sufficient condition on K is also necessary. When it is not satisfied may occur. Olevskii and Ulanovskii designed irregular sampling strategies which remedy . Then one can optimally reduce the number of measures needed to recover a signal or an image whose Fourier transform is supported by a compact set K with a given measure. The present contribution is aimed at bridging the gap between this advance on irregular sampling and the theory of quasicrystals.
68 citations
TL;DR: In this paper, the authors obtained irregular sampling theorems for the wavelet transform and the short-time Fourier transform, yielding irregular weighted frames for wavelets and Gabor functions with explicit estimates for the frame bounds.
Abstract: We obtain irregular sampling theorems for the wavelet transform and the short-time Fourier transform. These sampling theorems yield irregular weighted frames for wavelets and Gabor functions with explicit estimates for the frame bounds.
68 citations
TL;DR: The angular difference function (ADF) is presented and its applicability to rotation estimation is demonstrated and it is efficiently computed using the pseudopolar Fourier transform, which computes the discrete Fouriertransform of an image on a near spherical grid.
Abstract: The estimation of large motions without prior knowledge is an important problem in image registration. In this paper, we present the angular difference function (ADF) and demonstrate its applicability to rotation estimation. The ADF of two functions is defined as the integral of their spectral difference along the radial direction. It is efficiently computed using the pseudopolar Fourier transform, which computes the discrete Fourier transform of an image on a near spherical grid. Unlike other Fourier-based registration schemes, the suggested approach does not require any interpolation. Thus, it is more accurate and significantly faster.
68 citations
TL;DR: It is shown that the transformed sequence may be processed using a ROOT MUSIC based approach to estimate the elevations and azimuths of the observed sources.
Abstract: The problem of estimating the directions of arrival of narrowband plane waves impinging on a uniform circular array with M identical sensors uniformly distributed around a circle is considered. Specifically, the authors study a transformed data sequence that is equal to a reordering of the inverse discrete Fourier transform sequence corresponding to the outputs of a circular array with M elements uniformly distributed around the array circumference. It is shown that the transformed sequence may be processed using a ROOT MUSIC based approach to estimate the elevations and azimuths of the observed sources. Any root estimated via ROOT MUSIC which is on or close to the unit circle indicates the presence of a source at the elevation under consideration and an azimuth equal to the phase of the root. Experimental results are provided to demonstrate the advantages of processing the transformed data. >
67 citations
TL;DR: A novel Fourier technique for digital signal processing is developed based on the number-theoretic method of the Mobius inversion of series that competes with the classical FFT (fast Fourier transform) approach in terms of accuracy, complexity, and speed.
Abstract: A novel Fourier technique for digital signal processing is developed. This approach to Fourier analysis is based on the number-theoretic method of the Mobius inversion of series. The Fourier transform method developed is shown also to yield the convolution of two signals. A computer simulation shows that this method for finding Fourier coefficients is quite suitable for digital signal processing. It competes with the classical FFT (fast Fourier transform) approach in terms of accuracy, complexity, and speed. >
67 citations