Fourier components

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• Fourier analysis — In mathematics, Fourier analysis is a subject area which grew out of the study of Fourier series. The subject began with trying to understand when it was possible to represent general functions by sums of simpler trigonometric functions. The… …   Wikipedia

• Fourier optics — is the study of classical optics using techniques involving Fourier transforms and can be seen as an extension of the Huygens Fresnel principle. The underlying theorem that light waves can be described as made up of sinusoidal waves, in a manner… …   Wikipedia

• Fourier transform — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms The Fourier transform is a mathematical operation that decomposes a function into its constituent… …   Wikipedia

• Fourier principle — /fooˈri ā prinˈsi pl/ noun The principle showing that all repeating waveforms can be resolved into sine wave components consisting of a fundamental frequency and a series of harmonics at multiples of this frequency ORIGIN: Ety as for ↑Fourier… …   Useful english dictionary

• Fourier theorem — In mathematics, the Fourier theorem is a theorem stating that a periodic function f ( x ), which is reasonably continuous, may be expressed as the sum of a series of sine and cosine terms (called the Fourier series), each of which has specific… …   Wikipedia

• Discrete Fourier transform — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms In mathematics, the discrete Fourier transform (DFT) is a specific kind of discrete transform, used in… …   Wikipedia

• Relations between Fourier transforms and Fourier series — In the mathematical field of harmonic analysis, the continuous Fourier transform has very precise relations with Fourier series. It is also closely related to the discrete time Fourier transform (DTFT) and the discrete Fourier transform (DFT).… …   Wikipedia

• A derivation of the discrete Fourier transform — In mathematics, computer science, and electrical engineering, the discrete Fourier transform (DFT), occasionally called the finite Fourier transform, is a transform for Fourier analysis of finite domain discrete time signals. As with most Fourier …   Wikipedia

• Fast Fourier transform — A fast Fourier transform (FFT) is an efficient algorithm to compute the discrete Fourier transform (DFT) and its inverse. There are many distinct FFT algorithms involving a wide range of mathematics, from simple complex number arithmetic to group …   Wikipedia

• Discrete-time Fourier transform — In mathematics, the discrete time Fourier transform (DTFT) is one of the specific forms of Fourier analysis. As such, it transforms one function into another, which is called the frequency domain representation, or simply the DTFT , of the… …   Wikipedia

• Short-time Fourier transform — The short time Fourier transform (STFT), or alternatively short term Fourier transform, is a Fourier related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. STFT… …   Wikipedia