The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations

Jerri, Abdul J.

doi:10.1007/978-1-4757-2847-7

Cited by 154 publications

(89 citation statements)

References 54 publications

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“…cross sections obtained with this method often start abruptly at the threshold energy and are thus affected by the Gibbs phenomenon (Jerri 1998), which causes ringing artifacts around jump discontinuities in Fourier transforms, as illustrated in Fig. 3.…”

Section: Photodissociation Cross Sectionsmentioning

confidence: 99%

“…Whether or not Gibbs oscillations appear thus depends on several factors: the topology of the potential energy curves, their relative positions and the initial vibrational level. Although various filtering methods may be used to reduce these ringing artifacts (Jerri 1998), it is generally impossible to suppress them completely. It is however possible to do so in the present case using the total photodissociation cross section calculated from the autocorrelation function for short propagation times (Fig.…”

Section: Photodissociation Cross Sectionsmentioning

confidence: 99%

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Determination of photodissociation and radiative association cross sections from the same time-dependent calculation

Vranckx

Loreau

Desouter-Lecomte

et al. 2013

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. We illustrate some of the difficulties that may be encountered when computing photodissociation and radiative association cross sections from the same time-dependent approach based on wavepacket propagation. The total and partial photodissociation cross sections from the thirty-three vibrational levels of the b 3 Σ + state of HeH + towards the 9 other 3 Σ + and 6 3 Π n = 2, 3 higher-lying electronic states are calculated, using the autocorrelation method introduced by Heller (1978) and the method based on the asymptotic behaviour of wavepackets introduced by Balint-Kurti et al. (1990). The corresponding radiative association cross sections are extracted from the same calculations, and the photodissociation and radiative association rate constants are determined.

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Section: Photodissociation Cross Sectionsmentioning

confidence: 99%

Section: Photodissociation Cross Sectionsmentioning

confidence: 99%

Determination of photodissociation and radiative association cross sections from the same time-dependent calculation

Vranckx

Loreau

Desouter-Lecomte

et al. 2013

J. Phys. B: At. Mol. Opt. Phys.

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“…This oscillation behavior is a common phenomenon known as the Gibbs phenomenon that appears when the underlying function being approximated has jump discontinuities. Some methods have been suggested in the literature to reduce the effect of Gibbs phenomenon (see [13]). Another approach is to use a continuous approximation of the non smooth input signal as the new input for the system [20].…”

Section: Z(t)ẋ(t) = A(t)x(t) + B(t)u(t) T ∈mentioning

confidence: 99%

LS-SVM approximate solution to linear time varying descriptor systems

Mehrkanoon

Suykens

2012

Automatica

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This paper discusses a numerical method based on Least Squares Support Vector Machines (LS-SVMs) for solving linear time varying initial and boundary value problems in Differential Algebraic Equations (DAEs). The method generates a closed form (model-based) approximate solution. The results of numerical experiments on different systems with index from 0 to 3, are presented and compared with analytic solutions to confirm the validity and applicability of the proposed method.

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“…The conventional way to define the fuzzy filters is by generalizing the binary spatial-rank relation. Assume that a filter h is applied to a set Ω of neighboring samples x[m+m',n+n'] around the input x[m,n] to form the output (1) and its unbiased form with normalization (2) In (1), h[m+m',n+n'], x[m,n] controls the contribution of the input x[m+m',n+n'] to the output. For a linear filter, h is fixed and input-independent.…”

Section: Fuzzy Filtermentioning

confidence: 99%

“…Compressing block edges the correlation between pixels at the border of neighboring blocks and causes blocking artifacts individual. Due to the loss of high frequencies the ringing artifacts (similar to the Gibbs phenomenon [1]) occur when quantizing the DCT coefficients with a coarse quantization. On the other hand, mosquito artifacts come from ringing artifacts of compressed frames when displayed in a sequence.…”

Section: Introductionmentioning

confidence: 99%