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: Corrected successive integration methods in the literature are correct, but a more direct way of applying them which is called linear regression of the sum is offered which is recommended over FT-based methods, as the FT methods are more affected by noise in the original data.
Abstract: Several computational methods are presented for the rapid extraction of decay time constants from discrete exponential data. Two methods are found to be comparably fast and highly accurate. They are corrected successive integration and a method involving the Fourier transform (FT) of the data and the application of an expression that does not assume continuous data. FT methods in the literature are found to introduce significant systematic error owing to the assumption that data are continuous. Corrected successive integration methods in the literature are correct, but we offer a more direct way of applying them which we call linear regression of the sum. We recommend the use of the latter over FT-based methods, as the FT methods are more affected by noise in the original data.
67 citations
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: 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: 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
TL;DR: The techniques disclosed here should be especially important in real-time estimation of power spectra, in instances where the data sequence is essentially unterminated.
Abstract: A common application of the method of high speed convolution and correlation is the computation of autocorrelation functions, most commonly used in the estimation of power spectra. In this case the number of lags for which the autocorrelation function must be computed is small compared to the length of the data sequence available. The classic paper by Stockham, revealing the method of high speed convolution and correlation, also discloses a number of improvements in the method for the case where only a small number of lag values are desired, and for the case where a data sequence is extremely long. In this paper, the special case of autocorrelation is further examined. An important simplification is noted, based on the linearity of the discrete Fourier transform, and the circular shifting properties of discrete Fourier transforms. The techniques disclosed here should be especially important in real-time estimation of power spectra, in instances where the data sequence is essentially unterminated.
66 citations