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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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Fourier-Reihen und Fourier-Integral
1970Jeder Elektroniker hat sicher bereits so manches Werk uber Fourier-Reihen studiert. Jeder, der auf dem Gebiet der Elektrotechnik oder der Funktechnik arbeitet, hat eine gewisse Vorstellung von der qualitativen Beziehung zwischen der Grundfrequenz und den Oberschwingungen, welche die komplizierten Schwingungsformen erzeugen.
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Fourier and Fourier-Mehler Transforms
1993Recall that in Section 4.A we have the following J- and f-transformations defined on the space (f)* of generalized white noise functionals: for Ф∈(f)* and ξ∈f(ℝ),
Takeyuki Hida +3 more
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Fourier Integrals and Fourier Transforms
2009The concept of an infinite series dates back as far as the ancient Greeks such as Archimedes (287-212 b.c., who summed a geometric series in order to compute the area under a parabolic arc. In the eighteenth century, power series expansions for functions like e x , sin x, and arctan x were first published by the Scottish mathematician C.
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Fourier Analysis and Fourier Transform
2017The origins of Fourier analysis in science can be found in Ptolemy’s decomposing celestial orbits into cycles and epicycles and Pythagoras’ decomposing music into consonances. Its modern history began with the eighteenth century work of Bernoulli, Euler, and Gauss on what later came to be known as Fourier series. J.
Aparna Vyas, Soohwan Yu, Joonki Paik
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Fourier Series and Fourier Transform
1998In this chapter we look at some of the eigenfunction expansions in terms of Fourier series. We develop the Fourier transform and use it to solve the heat equation again. We also give a brief treatment of the discrete Fourier transform (DFT) and the fast Fourier transform (FFT).
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Fourier series and Fourier transforms
1992Abstract A familiarity with Fourier mathematics will be needed on several occasions throughout this book. We take the opportunity in this chapter to set out those mathematical properties that will be needed later. It is assumed that the reader has encountered both Fourier series and Fourier transforms before, but may not be entirely ...
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Concept, implementations and applications of Fourier ptychography
Nature Reviews Physics, 2021Guoan Zheng, Cheng Shen, Shaowei Jiang
exaly
Fourier-Reihen und Fourier-Integrale
2009Dieser Abschnitt befasst sich mit Fourier-Reihen: der Sinusreihe, der Kosinusreihe und der Exponentialreihe e ikx . Rechteckschwingungen (mit den Funktionswerten 1, 0 oder −1) sind grosartige Beispiele fur Funktionen mit Deltafunktionen in der Ableitung.
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