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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.


Papers
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Patent
Sung-kyu Choi1
19 Dec 1995
TL;DR: In this paper, a pair of scanners scan the respective transform coefficients output by the transform devices according to predetermined patterns, and a prediction is made as to which transform mode will produce the least amount of variable-length-code, and corresponding transform coefficients are selected to be sent to the variablelength-coder.
Abstract: An discrete cosine transform (DCT) apparatus is adaptive so as to choose between alternative transform modes for each successive pixel block to be transformed and subsequently variable-length-coded. A first transform device performs a DCT on a subject pixel block. A second transform device performs a DCT on the same subject pixel block of data which has been processed such that the frequency domain transformed data is distributed in a lower frequency compared with the transform coefficients produced by the first transform device. A pair of scanners scan the respective transform coefficients output by the transform devices according to predetermined patterns. A set of four counters accumulate information about the transform coefficients, as scanned by the scanners, so as to indicate the amount of data which would be produced by the respective sets of transform coefficients when variable-length-coded. Based upon the counts produced by the counters, a prediction is made as to which transform mode will produce the least amount of variable-length-code, and the corresponding transform coefficients are selected to be sent to the variable-length-coder.

27 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a numerical technique for the computation of Fourier transforms using a bilateral expansion of the unknown transformed function with respect to Laguarre functions using trigonometric interpolation and may be computed very efficiently by means of the Fast Fourier Transform.
Abstract: In this paper we propose a numerical technique for the computation of Fourier transforms. It uses a bilateral expansion of the unknown transformed function with respect to Laguarre functions. The expansion coefficients are obtained via trigonometric interpolation and may be computed very efficiently by means of the Fast Fourier Transform. The convergence of the algorithm is analyzed and numerical results are presented which confirm that it works well.

27 citations

Journal ArticleDOI
TL;DR: The concept of the A-wavelet transform can be extended for representation of other unitary transforms and an example for the Hartley transform is described, and the reconstruction formula is given.
Abstract: A new concept of the A-wavelet transform is introduced, and the representation of the Fourier transform by the A-wavelet transform is described. Such a wavelet transform uses a fully scalable modulated window but not all possible shifts. A geometrical locus of frequency-time points for the A-wavelet transform is derived, and examples are given. The locus is considered "optimal" for the Fourier transform when a signal can be recovered by using only values of its wavelet transform defined on the locus. The inverse Fourier transform is also represented by the A/sup */-wavelet transform defined on specific points in the time-frequency plane. The concept of the A-wavelet transform can be extended for representation of other unitary transforms. Such an example for the Hartley transform is described, and the reconstruction formula is given.

27 citations

Journal ArticleDOI
TL;DR: In this paper, a review of the properties of the fractional Fourier transform, which is used in information processing, is presented in connection with the symplectic tomography transform of optical signals.
Abstract: A review of the properties of the fractional Fourier transform, which is used in information processing, is presented in connection with the symplectic tomography transform of optical signals The relationship between the Green function of the quantum harmonic oscillator and the fractional Fourier transform is elucidated An analysis of electromagnetic signals which uses an invertible map of analytic signal onto the tomographic probability distribution is made The formal connection of the analysis with the tomography method of measuring quantum states is considered The relation to other methods of time-frequency quasidistributions (for example, the Ville-Wigner quasidistribution) characterizing a signal is studied

27 citations

Journal ArticleDOI
01 Oct 1971
TL;DR: An odd discrete Fourier transform (ODFT) which relates in several ways to the usual discrete Fouriers transform (DFT) is introduced and discussed and can readily be applied to spectrum and correlation computations on real signals.
Abstract: An odd discrete Fourier transform (ODFT) which relates in several ways to the usual discrete Fourier transform (DFT) is introduced and discussed. Its main advantage is that it can readily be applied to spectrum and correlation computations on real signals, by halving the storage capacity and greatly reducing the number of necessary steps.

27 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202318
202233
20213
20201
20191
20189