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.
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TL;DR: In this paper, it was shown that the distance densities that can arise from a many-body wave function lie in a convex set and that these densities have positive Fourier transforms.
17 citations
TL;DR: It is shown that for an analysis filter length that does not exceed a given value, the optimal synthesis scheme is independent of the duration of the given MDSTT and is an extension of the weighted overlap add (WOLA) synthesis method.
Abstract: The discrete short-time transform (DSTT) is a generalization of the discrete short-time Fourier transform (DSTFT). The necessary and sufficient conditions on the analysis filter, under which perfect reconstruction of the input signal is possible (when the DSTT is not modified), are presented. The class of linear modifications for which the original input can be reconstructed when the modification is applied is characterized. The synthesis of an optimal (in the minimum-mean-square-error sense) signal from a modified DSTT (MDSTT) of finite duration is presented. It is shown that for an analysis filter length that does not exceed a given value, the optimal synthesis scheme is independent of the duration of the given MDSTT and is an extension of the weighted overlap add (WOLA) synthesis method. For longer analysis filters, the optimal synthesis scheme becomes quite cumbersome, and therefore, a steady-state solution (as the duration of the MDSTT approaches infinity) is presented for this case. It is shown that this solution can be approximated with arbitrarily small reconstruction error. >
17 citations
TL;DR: This paper introduces a method for determining the locations of jump discontinuities, or edges, in a one-dimensional periodic piecewise-smooth function from nonuniform Fourier coefficients.
Abstract: Edge detection is important in a variety of applications. While there are many algorithms available for detecting edges from pixelated images or equispaced Fourier data, much less attention has been given to determining edges from nonuniform Fourier data. There are applications in sensing (e.g. MRI) where the data is given in this way, however. This paper introduces a method for determining the locations of jump discontinuities, or edges, in a one-dimensional periodic piecewise-smooth function from nonuniform Fourier coefficients. The technique employs the use of Fourier frames. Numerical examples are provided.
17 citations
07 Jun 1995
TL;DR: In this paper, the authors show that there are several uncertainty principles for the short-time Fourier transform and spectrogram, and they generalize the concept of the short time Fourier transformation to arbitrary variables.
Abstract: We show that there are a number of uncertainty principles for the short-time Fourier transform and spectrogram. Explicit expressions are derived and examples given. Also, we generalize the concept of the short-time Fourier transform to arbitrary variables.
17 citations
01 Oct 2016
TL;DR: With AWFT, this work is able to extract meaningful intrinsic localized orientation-sensitive structures on surfaces, and use them in applications such as shape segmentation, salient point detection, feature point description, and matching.
Abstract: We propose Anisotropic Windowed Fourier Transform (AWFT), a framework for localized space-frequency analysis of deformable 3D shapes. With AWFT, we are able to extract meaningful intrinsic localized orientation-sensitive structures on surfaces, and use them in applications such as shape segmentation, salient point detection, feature point description, and matching. Our method outperforms previous approaches in the considered applications.
17 citations