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Fast Fourier Transforms, Tworzenie gier, Resources, Water

[ Pobierz całość w formacie PDF ]
//-->Fast Fourier Transforms (FFTs)and Graphical Processing Units(GPUs)Kate DespainCMSC828e– p. 1/3Outline••••MotivationIntroduction to FFTs•Discrete Fourier Transforms (DFTs)•Cooley-Tukey AlgorithmCUFFT LibraryHigh Performance DFTs on GPUs by MicrosoftCorporation•Coalescing•Use of Shared Memory•Calculation-rich Kernels– p. 2/3Motivation: Uses of FFTs•Scientific Computing: Method to solvedifferential equationsFor example, in Quantum Mechanics (or Electricity &Magnetism) we often assume solutions to Schrodinger’sEquation (or Maxwell’s equations) to be plane waves,which are built on a Fourier basis∞A=k=−∞AeikxThen, ink-space,derivative operators becomemultiplications∂AikxAke=i∂xk=−∞∞– p. 3/3Motivation: Uses of FFTs••Digital Signal Processing & Image Processing•Receive signal in the time domain, but wantthe frequency spectrumConvolutions/Filters•Filter can be represented mathematically by aconvolution•Using the convolution theorem and FFTs,filters can be implemented efficientlyConvolution Theorem: The Fourier transform of aconvolution is the product of the Fourier transforms of theconvoluted elements.– p. 4/3Introduciton: What is an FFT?•Algorithm to compute Discrete FourierTransform (DFT)•Straightforward implementation requiresON2MADD operations2πixnexp−Xk=knNn=0N−1– p. 5/3 [ Pobierz całość w formacie PDF ]