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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.
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TL;DR: In this paper, a set of conditions has been developed under which a sequence is uniquely specified by the phase or samples of the phase of its Fourier transform, which are applicable to both one-dimensional and multi-dimensional sequences.
Abstract: Recently, a set of conditions has been developed under which a sequence is uniquely specified by the phase or samples of the phase of its Fourier transform. These conditions are distinctly different from the minimum or maximum phase requirement and are applicable to both one-dimensional and multi-dimensional sequences. Under the specified conditions, several numerical algorithms have been developed to reconstruct a sequence from its phase. In this paper, we review the recent theoretical results pertaining to the phase-only reconstruction problem, and we discuss in detail two iterative numerical algorithms for performing the reconstrucction.
34 citations
34 citations
TL;DR: A lens system that is able to perform equidistant fractional Fourier transforms that cover the whole range of orders and that consist of a minimum number of modules is introduced.
Abstract: The fractional Fourier transform is a new topic in optics. To make use of the fractional Fourier transform as an experimental tool, I design a fractional Fourier transformer of variable order: I introduce a lens system that is able to perform equidistant fractional Fourier transforms that cover the whole range of orders and that consist of a minimum number of modules. By module, I mean an elementary fractional Fourier transform of certain order that consists of a lens between two free-space lengths. Because of the commutative additivity of the transform, various fractional orders can be achieved by means of different constellations of the modules. It is possible to perform a large variety of fractional Fourier transforms with a small number of modules.
34 citations
01 Apr 2002
TL;DR: In this paper, the authors introduce the notion of fractional Fourier transform, which may be considered as a fractional power of the classical Fourier trans-form, and give an introduction to the denition, the properties and computational aspects of both the continuous and discrete Fourier transforms.
Abstract: In this survey paper we introduce the reader to the notion of the fractional Fourier transform, which may be considered as a fractional power of the classical Fourier trans- form. It has been intensely studied during the last decade, an attention it may have partially gained because of the vivid interest in time-frequency analysis methods of signal processing, like wavelets. Like the complex exponentials are the basic functions in Fourier analysis, the chirps (signals sweeping through all frequencies in a certain interval) are the building blocks in the fractional Fourier analysis. Part of its roots can be found in optics where the fractional Fourier transform can be physically realized. We give an introduction to the denition, the properties and computational aspects of both the continuous and discrete fractional Fourier transforms. We include some examples of applications and some possible generalizations.
34 citations
TL;DR: A fast algorithm is proposed to compute the discrete Hilbert transform via the fast Hartley transform (FHT), where the computation complexity can be greatly reduced from two complex FFTs into two real FHTs.
Abstract: A fast algorithm is proposed to compute the discrete Hilbert transform via the fast Hartley transform (FHT). Instead of the conventional fast Fourier transform (FFT) approach, the processing is carried out entirely in the real domain. Also, since many efficient FHT algorithms exist, the computation complexity can be greatly reduced from two complex FFTs into two real FHTs. >
34 citations