Results 271 to 280 of about 303,830 (309)
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2018
The FT version of the Fourier analysis is presented. FT is the most general version of the Fourier analysis and it is capable of representing all types of signals. However, it is mostly used to represent continuous aperiodic signals by continuous aperiodic spectra. The FT is derived starting from the FS definition. Examples of finding the FT of signals
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The FT version of the Fourier analysis is presented. FT is the most general version of the Fourier analysis and it is capable of representing all types of signals. However, it is mostly used to represent continuous aperiodic signals by continuous aperiodic spectra. The FT is derived starting from the FS definition. Examples of finding the FT of signals
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Review of Scientific Instruments, 1987
We describe a scanning Michelson interferometer and utilization of fast Fourier transformation in laser wavelength determination. The Fourier transformation method is demonstrated to be particularly powerful in cw multimode (diode) laser investigations and in cw single-mode laser long-term frequency stability measurements. An uncertainty less than 10−7
Junttila, Marja-Leena +5 more
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We describe a scanning Michelson interferometer and utilization of fast Fourier transformation in laser wavelength determination. The Fourier transformation method is demonstrated to be particularly powerful in cw multimode (diode) laser investigations and in cw single-mode laser long-term frequency stability measurements. An uncertainty less than 10−7
Junttila, Marja-Leena +5 more
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Fourier Integrals and Fourier Transforms
2014In the preceding chapter ″Fourier series″ we showed that an arbitrary periodic function with period T can be described as the sum of trigonometric functions with multiples of the period T.
Klaus Weltner +4 more
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1998
The Fourier transformation of a function u∈ℒ’ is defined by $$ \hat u\left( \xi \right) = \int {{e^{ - i\left\langle {x,\xi } \right\rangle }}} u(x)dx. $$ In Section 7.1 we extend the definition to all u∈ℒ’ the space of temperate distributions, which is the smallest subspace of D’ containing L1 which is invariant under differentiation and ...
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The Fourier transformation of a function u∈ℒ’ is defined by $$ \hat u\left( \xi \right) = \int {{e^{ - i\left\langle {x,\xi } \right\rangle }}} u(x)dx. $$ In Section 7.1 we extend the definition to all u∈ℒ’ the space of temperate distributions, which is the smallest subspace of D’ containing L1 which is invariant under differentiation and ...
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Fourier Series and Fourier Transforms
2003In Chapter 3, we touched upon the analogy between the diffraction of x-rays and that of visible light. Here, we extend that discussion and consider some aspects of Fourier series and Fourier transforms.
Mark Ladd, Rex A. Palmer
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On the Fourier series and Fourier transforms
Journal of Mathematical Sciences, 2019This survey article is addresses to classical harmonic analysis. In particular, a number of classical theorems are presented with the simplest, in our opinion, proofs (see also [1] and references therein). Some results of the present article are new and are published for the first time.
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Diskrete Fourier-Transformation
2017Diskrete Fourier-Transformation trigonometrischer Vektoren Inverse der Sinus-Transformation Ablauf des FFT-Algorithmus Trigonometrische Interpolation an aquidistanten Stutzstellen Eigenwerte und Inverse einer zyklischen Matrix Zyklisches lineares Gleichungssystem Approximation von Fourier-Koeffzienten mit Riemann ...
Klaus Höllig, Jörg Hörner
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1995
Publisher Summary This chapter focuses on the Fourier transforms. The chapter reviews the Fourier exponential transform and the basic properties of the Fourier transforms. Some elementary Fourier transform pairs are presented in a tabulated form. It may either be used to find the Fourier transform F(ω) of a function f(x) or, conversely, to find the ...
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Publisher Summary This chapter focuses on the Fourier transforms. The chapter reviews the Fourier exponential transform and the basic properties of the Fourier transforms. Some elementary Fourier transform pairs are presented in a tabulated form. It may either be used to find the Fourier transform F(ω) of a function f(x) or, conversely, to find the ...
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Concept, implementations and applications of Fourier ptychography
Nature Reviews Physics, 2021Guoan Zheng, Cheng Shen, Shaowei Jiang
exaly
, 2021