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The name "butterfly" comes from the shape of the data-flow diagram in the radix-2 case, as described below. [1] The earliest occurrence in print of the term is thought to be in a 1969 MIT technical report. [2] [3] The same structure can also be found in the Viterbi algorithm, used for finding the most likely sequence of hidden states.
Functions of this form are known as Bloch functions or Bloch states, and serve as a suitable basis for the wave functions or states of electrons in crystalline solids. The description of electrons in terms of Bloch functions, termed Bloch electrons (or less often Bloch Waves ), underlies the concept of electronic band structures .
Transposed Block Face-splitting product in the model of a Multi-Face radar with DAA, proposed by V. Slyusar in 1996 [5]. The main approach to digital signal processing in DAA is the "digital beamforming" after Analog-to-digital converters (ADC) of receiver channels or before Digital-to-analog converters (DAC) by transmission.
Analysis of plane wave scattering from a subwavelength plasmonic grating with RCWA method. Rigorous coupled-wave analysis (RCWA), also known as Fourier modal method (FMM), [1] is a semi-analytical method in computational electromagnetics that is most typically applied to solve scattering from periodic dielectric structures.
A useful property of the DFT is that the inverse DFT can be easily expressed in terms of the (forward) DFT, via several well-known "tricks". (For example, in computations, it is often convenient to only implement a fast Fourier transform corresponding to one transform direction and then to get the other transform direction from the first.)
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). A Fourier transform converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa.
Bloch's theorem was inspired by the following theorem of Georges Valiron: Theorem. If f is a non-constant entire function then there exist disks D of arbitrarily large radius and analytic functions φ in D such that f(φ(z)) = z for z in D. Bloch's theorem corresponds to Valiron's theorem via the so-called Bloch's principle.
A twiddle factor, in fast Fourier transform (FFT) algorithms, is any of the trigonometric constant coefficients that are multiplied by the data in the course of the algorithm. This term was apparently coined by Gentleman & Sande in 1966, and has since become widespread in thousands of papers of the FFT literature.