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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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Journal ArticleDOI
TL;DR: This work considers the problem of fast computation of the Fourier transform over a finite field by decomposing an arbitrary polynomial into a sum of linearized polynomials.
Abstract: We consider the problem of fast computation of the Fourier transform over a finite field by decomposing an arbitrary polynomial into a sum of linearized polynomials. Examples of algorithms for the Fourier transform with complexity less than that of the best known analogs are given.

61 citations

Journal ArticleDOI
TL;DR: In this paper, the authors prove orthogonality relations for some analogs of trigonometric functions on a g-quadratic grid and introduce the corresponding g-Fourier series.
Abstract: We prove orthogonality relations for some analogs of trigonometric functions on a g-quadratic grid and introduce the corresponding g-Fourier series. We also discuss several other properties of this basic trigonometric system and the g-Fourier series.

61 citations

Journal ArticleDOI
TL;DR: A double image encryption method is proposed by utilizing discrete multiple-parameter fractional Fourier transform and chaotic maps to encrypt two original images scrambled by one chaotic map with one original image as its phase.

61 citations

Journal ArticleDOI
TL;DR: The Walsh power spectrum of a sequence of random samples is defined as the Walsh transform of the logical autocorrelation function of the random sequence and the Fourier power spectrum can be obtained from the Walsh power Spectrum by a linear transformation.
Abstract: The Walsh power spectrum of a sequence of random samples is defined as the Walsh transform of the logical autocorrelation function of the random sequence. The "logical" autocorrelation function is defined in a similar form as the "arithmetic" autocorrelation function. The Fourier power spectrum, which is defined as the Fourier transform of the arithmetic autocorrelation function, can be obtained from the Walsh power spectrum by a linear transformation. The recursive relations between the logical and arithmetic auto-correlation functions are derived in this paper. For a given process with computed or modeled autocorrelation function the Fourier and Walsh power spectra are computed by using the fast Fourier and Walsh transforms, respectively. Examples are given from the speech and imagery data.

61 citations

Journal ArticleDOI
TL;DR: This paper first proposes a generalized convolution theorem for the LCT and then derives a corresponding product theorem associated with the L CT, which is shown to be special cases of the derived results.
Abstract: The linear canonical transform (LCT), which is a generalized form of the classical Fourier transform (FT), the fractional Fourier transform (FRFT), and other transforms, has been shown to be a powerful tool in optics and signal processing. Many results of this transform are already known, including its convolution theorem. However, the formulation of the convolution theorem for the LCT has been developed differently and is still not having a widely accepted closed-form expression. In this paper, we first propose a generalized convolution theorem for the LCT and then derive a corresponding product theorem associated with the LCT. The ordinary convolution theorem for the FT, the fractional convolution theorem for the FRFT, and some existing convolution theorems for the LCT are shown to be special cases of the derived results. Moreover, some applications of the derived results are presented.

60 citations


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