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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 ...
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2018
In the previous chapter, we observed a peculiar relation between the smoothness and the rapidity of vanishing at infinity of a function f, as well as its Fourier transform \(\hat {f}\). Based upon this observation, we introduce an important function space \(\mathfrak {S}\), which is invariant under the Fourier transforms. We then proceed to \(\mathfrak
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In the previous chapter, we observed a peculiar relation between the smoothness and the rapidity of vanishing at infinity of a function f, as well as its Fourier transform \(\hat {f}\). Based upon this observation, we introduce an important function space \(\mathfrak {S}\), which is invariant under the Fourier transforms. We then proceed to \(\mathfrak
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Fourier transform Raman spectroscopy
Mikrochimica Acta, 1986The basic experimental aspects of Fourier transform Raman Spectroscopy are reviewed with an emphasis on detector technology. The sensitivity is comparable to dispersive Raman Spectroscopy using visible lasers. The ease of spectral subtraction is demonstrated and examples are given showing the elimination of fluorescence.
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Diskrete Fourier-Transformation und Fast Fourier Transform
2017Handelt es sich bei der Zeitfunktion x = x(t) um eine analytisch nicht darstellbare Funktion, lasst sich die Fourier-Transformation nur numerisch bewerkstelligen. Voraussetzung ist, dass x(t) eine periodische Funktion ist (Abb. 33.1). Handelt es sich bei x(t) um eine aperiodische Funktion, gelingt nur eine Naherung, indem eine fiktive Periode T ...
Christian Petersen, Horst Werkle
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Fourier Transform, Short-Time Fourier Transform, and Wavelet Transform
2018This chapter presents information about the Fourier transform (FT), short-time Fourier transform (STFT), and wavelet transform. This chapter also covers use of this transform in speech signal processing.
Komal R. Borisagar +2 more
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DieKurzzeit-Fourier-Transformation
2020In der Analyse von instationaren Prozessen, wie zum Beispiel Sprach- oder Musiksignalen, mochte man haufig Aufschluss uber die im Signal enthaltenen Spektralanteile gewinnen und diese zu Zeitpunkten bzw. Zeitintervallen zuordnen. Das bedeutet, man sucht eine Darstellung, in der die Signalanteile wie bei einem Notenblatt bezuglich ihres zeitlichen ...
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Fourier Transforms and Fourier Transforms N.M.R.
2023Gwenola Burgot, Jean-Louis Burgot
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Integrated photodetectors for compact Fourier-transform waveguide spectrometers
Nature Photonics, 2022Matthias J Grotevent +2 more
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