Fourier series
- noun
- /ˈfʊrieɪ ˈsɪriz/
- Specialized
:
serie de Fourier
- The Fourier series allows us to express a periodic function as the sum of sine and cosine terms.
OK, but again, this doesn't imply that the Fourier series converges to F uniformly.
- OK, but again, this doesn't imply that the Fourier series converges to F uniformly.
- And that's where a Fourier series can come in.
Examples
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And if these so, you know, the Fourier series, I can always decompose the signal into a series of harmonics, periodic signal.
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And so it's the discrete time Fourier series that has a duality.
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So the analysis is the Fourier series is forming.
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Then the question was, what's the Fourier series of DF DX?
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Fourier series.
Academic text (1991) -
Now capital Phi being such a nice function, has a Fourier series expand Phi capital Phi that is in the Fourier series.
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In signal processing, we often use the Fourier series to analyze periodic signals.
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Mathematicians use the Fourier series to break down complex waveforms into simpler components.
Synonyms
1
9.0
A method that breaks a repeating signal into simple sine and cosine waves
To break a repeating sound or signal into simple waves like sine and cosine
Surface Forms
Morphology
Although 'series' signals a mathematical sum, the specific meaning — a decomposition into sine and cosine terms associated with the mathematician Fourier — relies on specialized mathematical knowledge or familiarity with the name 'Fourier'. A B1 learner who knows the words 'Fourier' (a proper name) and 'series' will not be able to derive the technical concept of periodic-function decomposition from the constituents alone, so the expression is not compositionally transparent.
Etymology
Fourier series is named after Joseph Fourier, who showed that a repeating wave or signal can be built by adding simple sine and cosine waves. Imagine making a complex sound by stacking clear tones; that's why Fourier series means 'writing a repeating wave by adding simple waves'.