&lt;title&gt;Physical wavelets: applications in optics&lt;/title&gt;

Deschênes, Sylvain; Sheng, Yunlong

doi:10.1117/12.458750

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Simple Asymptotics Of the Wavelet1

Introduction1

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2007

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“…which follows from (19) if y = 0, we get Re(s) > 1 outside the point x = ct, y = 0. Formulae ( 13), (14) show that s = 1 if x = ct, y = 0, which is the point of the maximum of the modulus of exponent (21). Hence, Re(s) 1, next Re(ps) 1 and the asymptotics ( 21) can be used.…”

Section: Simple Asymptotics Of the Waveletmentioning

confidence: 99%

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New physical wavelet ‘Gaussian wave packet’

Perel¹,

Sidorenko²

2007

J. Phys. A: Math. Theor.

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An exact solution of the homogeneous wave equation, which was found previously, is treated from the point of view of continuous wavelet analysis (CWA). If time is a fixed parameter, the solution represents a new multidimensional mother wavelet for the CWA. Both the wavelet and its Fourier transform are given by explicit formulas and are exponentially localized. The wavelet is directional. The widths of the wavelet and the uncertainty relation are investigated numerically. If a certain parameter is large, the wavelet behaves asymptotically as the Morlet wavelet. The solution is a new physical wavelet in the definition of Kaiser, it may be interpreted as a sum of two parts: an advanced and a retarded part, both being fields of a pulsed point source moving at a speed of wave propagation along a straight line in complex space-time.

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Section: Simple Asymptotics Of the Waveletmentioning

confidence: 99%

“…The physical wavelet as a localized solution of the wave equation has also been given in [10]. Applications of physical wavelets were discussed in [11]- [16].…”

Section: Introductionmentioning

confidence: 99%

New physical wavelet ‘Gaussian wave packet’

Perel¹,

Sidorenko²

2007

J. Phys. A: Math. Theor.

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<title>Physical wavelets: applications in optics</title>

Cited by 1 publication

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New physical wavelet ‘Gaussian wave packet’

New physical wavelet ‘Gaussian wave packet’

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