Topic
Discrete-time Fourier transform
About: Discrete-time Fourier transform is a research topic. Over the lifetime, 5072 publications have been published within this topic receiving 144643 citations. The topic is also known as: DTFT.
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TL;DR: In this article, the authors extend the fractional Fourier transform to different spaces of generalized functions using two different techniques, one analytic and the other algebraic, which makes the transform of a convolution of two functions almost equal to the product of their transform.
Abstract: In recent years the fractional Fourier transform (FRFT), which is a generalization of the Fourier transform, has been the focus of many research papers because of its application in several areas, including signal processing and optics. In this paper, we extend the fractional Fourier transform to different spaces of generalized functions using two different techniques, one analytic and the other algebraic. The algebraic approach requires the introduction of a new convolution operation for the fractional Fourier transform that makes the transform of a convolution of two functions almost equal to the product of their transform.
67 citations
TL;DR: In this paper, an azimuth convolution between a near-field focusing function and the frequency domain backscattered fields is discussed, which is efficiently implemented by using fast Fourier transform (FFT) techniques.
Abstract: This paper presents a new three-dimensional (3-D) near-field inverse synthetic aperture radar (ISAR) imaging technique. A 3-D ISAR image can be obtained by processing coherently the backscattered fields as a function of the frequency and two rotation angles about axes which are mutually orthogonal. Most of the existing ISAR algorithms are based on the Fourier transform and as such can tolerate only small amounts of wavefront curvature. Wavefront curvature must be taken into account when imaging an object in the near-field. Near-field ISAR imaging of large objects using a direct Fourier inversion may result in images which are increasingly unfocused at points which are more distant from the center of rotation. An algorithm based on an azimuth convolution between a near-field focusing function and the frequency domain backscattered fields is discussed. This convolution is efficiently implemented by using fast Fourier transform (FFT) techniques. Furthermore, in order to further alleviate the computational load of the algorithm, the discrete Fourier transform (DFT) of the focusing function is evaluated by means of the stationary phase method. Experimental results show that this technique is precise and virtually impulse invariant.
67 citations
TL;DR: From this solution an efficient numerical procedure is derived for synthesis of discrete-interval, binary, periodic signals the Fourier amplitude spectrum of which is optimal in the same sense.
Abstract: A closed-form solution is presented for the discrete-interval, binary, periodic signal the complex Fourier coefficient spectrum of which optimally approximates in the least squares sense a desired complex Fourier coefficient spectrum. From this solution an efficient numerical procedure is derived for synthesis of discrete-interval, binary, periodic signals the Fourier amplitude spectrum of which is optimal in the same sense. Numerical examples show the practical feasibility of the procedure.
67 citations
TL;DR: Using three‐dimensional ‘bright‐field’ imaging, single nano‐segregations were isolated from the surrounding matrix of an iron–copper alloy and measurement of the inner concentration within clusters is straightforward.
Abstract: Because of the increasing number of collected atoms (up to millions) in the three-dimensional atom probe, derivation of chemical or structural information from the direct observation of three-dimensional images is becoming more and more difficult. New data analysis tools are thus required. Application of a discrete Fourier transform algorithm to three-dimensional atom probe datasets provides information that is not easily accessible in real space. Derivation of mean particle size from Fourier intensities or from three-dimensional autocorrelation is an example. These powerful methods can be used to detect and image nano-segregations. Using three-dimensional 'bright-field' imaging, single nano-segregations were isolated from the surrounding matrix of an iron-copper alloy. Measurement of the inner concentration within clusters is, therefore, straightforward. Theoretical aspects related to filtering in reciprocal space are developed.
66 citations
TL;DR: In this article, a continuous wavelet transform (CWT) is used for phase-shift map computation in laser plasma interferograms. But, it can fail to produce accurate phase shift maps when low-quality images are dealt with.
Abstract: Laser plasma interferograms are currently analyzed by extraction of the phase-shift map with fast Fourier transform (FFT) techniques [Appl. Opt. 18, 3101 (1985)]. This methodology works well when interferograms are only marginally affected by noise and reduction of fringe visibility, but it can fail to produce accurate phase-shift maps when low-quality images are dealt with. We present a novel procedure for a phase-shift map computation that makes extensive use of the ridge extraction in the continuous wavelet transform (CWT) framework. The CWT tool is flexible because of the wide adaptability of the analyzing basis, and it can be accurate because of the intrinsic noise reduction in the ridge extraction. A comparative analysis of the accuracy performances of the new tool and the FFT-based one shows that the CWT-based tool produces phase maps considerably less noisy and that it can better resolve local inhomogeneties.
66 citations