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Wybierz jezyk: ar id bg ca ... zh Fourier analysis From Wikipedia, the free encyclopedia Jump to: navigation search Fourier transforms Continuous Fourier transform ... Related transforms Fourier analysis , named after Joseph Fourier 's introduction of the Fourier series , is the decomposition of a function in terms of sinusoidal functions (called basis functions ) of different frequencies that can be recombined to obtain the original function. The recombination process is called Fourier synthesis (in which case, Fourier analysis refers specifically to the decomposition process). The result of the decomposition is the amount (i.e. amplitude) and the phase to be imparted to each basis function (each frequency) in the reconstruction. It is therefore also a function (of frequency), whose value can be represented as a complex number , in either polar or rectangular coordinates. And it is referred to as the frequency domain representation of the original function. A useful analogy is the waveform produced by a musical chord and the set of musical notes (the frequency components) that it comprises. The term Fourier transform can refer to either the frequency domain representation of a function or to the process/formula that " transforms " one function into the other. However, the transform is usually given a more specific name depending upon the domain and other properties of the function being transformed, as elaborated below. Moreover, the original concept of Fourier analysis has been extended over time to apply to more and more abstract and general situations, and the general field is often known as | |
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