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The Fourier Series and Fourier Transform
2020We encountered the Fourier series in passing in Chap. 5. Then it was just to illustrate the importance of sine waves as a fundamental waveform from which more complex ones such as a square wave could be constructed by adding them with different frequencies and amplitudes.
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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 Series and the Fourier Transform
2016This chapter is entirely devoted to Fourier series and Fourier transforms, given their place and role in analysis, in mathematics, and in applications, especially in physics and engineering.
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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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Concept, implementations and applications of Fourier ptychography
Nature Reviews Physics, 2021G. Zheng +4 more
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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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Mathematics of the USSR-Sbornik, 1981
Let be an orthonormal system of functions on the interval , and let the function . We investigate the question of the convergence or divergence (depending on the smoothness of the function ) of series of the form where or with .It is shown that in a certain sense, the assertions obtained are definitive for the Haar system.Bibliography: 14 titles.
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Let be an orthonormal system of functions on the interval , and let the function . We investigate the question of the convergence or divergence (depending on the smoothness of the function ) of series of the form where or with .It is shown that in a certain sense, the assertions obtained are definitive for the Haar system.Bibliography: 14 titles.
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Scientific American, 1989
To calculate a transform, just listen. The ear automatically performs the calculation, which the intellect can execute only after years of mathematical education. The ear formulates a transform by converting sound-the waves of pressure traveling through time and the atmosphere-into a spectrum, a description of the sound as a series of volumes at ...
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To calculate a transform, just listen. The ear automatically performs the calculation, which the intellect can execute only after years of mathematical education. The ear formulates a transform by converting sound-the waves of pressure traveling through time and the atmosphere-into a spectrum, a description of the sound as a series of volumes at ...
openaire +2 more sources