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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.


Papers
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30 Nov 1998
TL;DR: In this article, the NDFT was used to construct a 1-D and 2-D antenna pattern synthesis with Prescribed Nulls, and the Dual-Tone Multi-Frequency Signal Decoding (DTMSD) was proposed.
Abstract: 1. Introduction. 2. The Nonuniform Discrete Fourier Transform. 3. 1-D Fir Filter Design Using the NDFT. 4. 2-D Fir Filter Design Using the NDFT. 5. Antenna Pattern Synthesis with Prescribed Nulls. 6. Dual-Tone Multi-Frequency Signal Decoding. 7. Conclusions. References. Index.

79 citations

Journal ArticleDOI
TL;DR: The adaptation of an iterative Fourier transform algorithm for the calculation of theoretical spectral phase functions required for pulse shaping applications and is shown to converges much faster than both alternative methods.
Abstract: We demonstrate the adaptation of an iterative Fourier transform algorithm for the calculation of theoretical spectral phase functions required for pulse shaping applications. The algorithm is used to determine the phase functions necessary for the generation of different temporal intensity profiles. The performance of the algorithm is compared to two exemplary standard approaches. i.e. a Genetic Algorithm and a combination of a Simplex Downhill and a Simulated Annealing algorithm. It is shown that the iterative Fourier transform algorithm converges much faster than both alternative methods.

78 citations

Journal ArticleDOI
TL;DR: This new, so-called recursive cyclotomic factorization algorithm (RCFA) is more efficient than the fast Fourier transformation (FFT) algorithm and can also be easily implemented, using only a limited number of different computation cells.
Abstract: In this paper, a new recursive algorithm for calculating the discrete Fourier transformation is presented. This new, so-called recursive cyclotomic factorization algorithm (RCFA) is more efficient than the fast Fourier transformation (FFT) algorithm. Moreover, due to its recursive nature, the RCFA can also be easily implemented, using only a limited number of different computation cells.

78 citations

Journal ArticleDOI
TL;DR: In this article, the authors define a discrete fractional Fourier transform (FT) which is essentially the time-evolution operator of the discrete harmonic oscillator, and define its energy eigenfunctions as a discrete algebraic analogue of the Hermite-Gaussian functions.
Abstract: Certain solutions to Harper's equation are discrete analogues of (and approximations to) the Hermite-Gaussian functions. They are the energy eigenfunctions of a discrete algebraic analogue of the harmonic oscillator, and they lead to a definition of a discrete fractional Fourier transform (FT). The discrete fractional FT is essentially the time-evolution operator of the discrete harmonic oscillator.

78 citations

Journal ArticleDOI
TL;DR: This paper derives the requisite polar version of the standard Fourier operations for convolution-two dimensional, circular, and radial one dimensional-and shows that standard multiplication/convolution rules do apply as long as the correct definition of convolution is applied.
Abstract: For functions that are best described in terms of polar coordinates, the two-dimensional Fourier transform can be written in terms of polar coordinates as a combination of Hankel transforms and Fourier series-even if the function does not possess circular symmetry. However, to be as useful as its Cartesian counterpart, a polar version of the Fourier operational toolset is required for the standard operations of shift, multiplication, convolution, etc. This paper derives the requisite polar version of the standard Fourier operations. In particular, convolution-two dimensional, circular, and radial one dimensional-is discussed in detail. It is shown that standard multiplication/convolution rules do apply as long as the correct definition of convolution is applied.

78 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202321
202249
20216
202015
201917
201834