Search results
Results From The WOW.Com Content Network
The Fourier number can be derived by nondimensionalizing the time-dependent diffusion equation.As an example, consider a rod of length that is being heated from an initial temperature by imposing a heat source of temperature > at time = and position = (with along the axis of the rod).
The Fourier series of a complex-valued P-periodic function (), integrable over the interval [,] on the real line, is defined as a trigonometric series of the form =, such that the Fourier coefficients are complex numbers defined by the integral [15] [16] = .
A number of authors, notably Jean le Rond d'Alembert, and Carl Friedrich Gauss used trigonometric series to study the heat equation, [20] but the breakthrough development was the 1807 paper Mémoire sur la propagation de la chaleur dans les corps solides by Joseph Fourier, whose crucial insight was to model all functions by trigonometric series ...
The number-theoretic transform (NTT) [4] is obtained by specializing the discrete Fourier transform to = /, the integers modulo a prime p. This is a finite field , and primitive n th roots of unity exist whenever n divides p − 1 {\displaystyle p-1} , so we have p = ξ n + 1 {\displaystyle p=\xi n+1} for a positive integer ξ .
Jean-Baptiste Joseph Fourier (/ ˈ f ʊr i eɪ,-i ər /; [1] French: [ʒɑ̃ batist ʒozɛf fuʁje]; 21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre, Burgundy and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and ...
The Fourier number (also known as the Fourier modulus), a ratio / of the rate of heat conduction to the rate of thermal energy storage Fourier-transform spectroscopy , a measurement technique whereby spectra are collected based on measurements of the temporal coherence of a radiative source
The Biot number increases as the Fourier number decreases. There are five steps to determine a temperature profile in terms of time. Calculate the Biot number; Determine which relative depth matters, either x or L. Convert time to the Fourier number. Convert to relative temperature with the boundary conditions.
An example application of the Fourier transform is determining the constituent pitches in a musical waveform.This image is the result of applying a constant-Q transform (a Fourier-related transform) to the waveform of a C major piano chord.