Topic
Discrete sine transform
About: Discrete sine transform is a research topic. Over the lifetime, 3269 publications have been published within this topic receiving 73181 citations.
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01 Jan 1988
TL;DR: In this article, the multiplicative complexity of the discrete Fourier transform (DFT) was analyzed and the complexity of DFT for any positive integer was shown. But the complexity was not shown for any integer.
Abstract: In this chapter the multiplicative complexity of the discrete Fourier transform (DFT) is analyzed. The next several sections define the DFT and then show how the complexity of the DFT is determined when the number of inputs is prime, a power of an odd prime, a power of two, and finally for any positive integer.
18 citations
TL;DR: In this article, the performance of discrete Fourier transform (DFT)-based algorithms employed in signal-to-noise-ratio (SNR) testing of waveform digitizers is analyzed and compared to the performance obtained using sine-fit procedures.
Abstract: The performance of discrete Fourier transform (DFT)-based algorithms employed in signal-to-noise-ratio (SNR) testing of waveform digitizers is analyzed and compared to the performance obtained using sine-fit procedures. Theoretical results are recalled, emphasizing their relevance and importance. Evaluations based on experimental data, obtained by an 8-bit digitizing oscilloscope, show that the accuracies approaches are comparable, while in several respects the methods appear complementary, rather than alternative.
18 citations
TL;DR: In this paper, a matrix multiplication procedure for evaluating the pixelated version of the near-field pattern of a discrete, one- or two-dimensional input is described, where the phase matrix is evaluated at ϵ=1.
Abstract: We describe a matrix multiplication procedure for evaluating the pixelated version of the near-field pattern of a discrete, one- or two-dimensional input. We show that for an input with N×N pixels, in an area d×d, it is necessary to evaluate the Fresnel diffraction pattern at distances z⩾d2/λN. Our numerical algorithm is also useful for evaluating the fractional Fourier transform by multiplying by a special phase matrix with fractional parameter ϵ. If the phase matrix is evaluated at ϵ=1, we find the discrete Fourier transform matrix.
18 citations
01 Jan 2007
TL;DR: In this article, the authors show that the eigenvectors in the limit converge to Gauss-Hermite functions and that the Eigenvalue spectrum of the commutor provides a good approximation to the continuous G-H differential operator.
Abstract: Existing approaches tofurnishing abasis ofeigenvectors for thediscrete Fourier transform (DFT)arebasedupondefiningtridiagonal operators thatcommutewiththeDFT.In this paper, motivated byideas fromquantummechanics in finite dimensions, wedefine asymmetric matrixthatcommuteswiththecentered DFT,thereby furnishing abasis of eigenvectors fortheDFT.We showthatthese eigenvectors inthelimit converge toGauss-Hermite (G-H)functions and thattheeigenvalue spectrum ofthecommutorprovides a verygooddiscrete approximation tothatofthecontinuous G-Hdifferential operator.
18 citations
TL;DR: In this article, the theory of the discrete Fourier transform is applied in solving a system of difference equations describing the positions of atoms in a deformed crystal lattice, which is approximated by the Born-Karman model modified to include the internal energy of the undeformed crystal.
Abstract: The theory of the discrete Fourier transform [1], [2] is applied in solving a system of difference equations describing the positions of atoms in a deformed crystal lattice. The crystal lattice is approximated by the Born-Karman model modified to include the internal energy of the undeformed crystal.
18 citations