IntroFFT

IntroFFT - 18-791 Lecture #17INTRODUCTION TO THE FAST...

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Unformatted text preview: 18-791 Lecture #17INTRODUCTION TO THE FAST FOURIER TRANSFORM ALGORITHMDepartment of Electrical and Computer EngineeringCarnegie Mellon UniversityPittsburgh, Pennsylvania 15213Phone: +1 (412) 268-2535FAX: +1 (412) 268-3890rms@cs.cmu.eduhttp://www.ece.cmu.edu/~rmsOctober 24, 2005Richard M. SternCarnegieMellonSlide 2ECE DepartmentIntroductionToday we will begin our discussion of the family of algorithms known as Fast Fourier Transforms, which have revolutionized digital signal processingWhat is the FFT?A collection of tricks that exploit the symmetry of the DFT calculation to make its execution much fasterSpeedup increases with DFT sizeToday - will outline the basic workings of the simplest formulation, the radix-2 decimation-in-time algorithmThursday - will discuss some of the variations and extensionsAlternate structuresNon-radix 2 formulationsCarnegieMellonSlide 3ECE DepartmentIntroduction, continuedSome dates:~1880 - algorithm first described by Gauss1965 - algorithm rediscovered (not for the first time) by Cooley and Tukey In 1967 (spring of my freshman year), calculation of a 8192-point DFT on the top-of-the line IBM 7094 took .~30 minutes using conventional techniques~5 seconds using FFTsCarnegieMellonSlide 4ECE DepartmentMeasures of computational efficiencyCould considerNumber of additionsNumber of multiplicationsAmount of memory requiredScalability and regularityFor the present discussion well focus most on number of multiplications as a measure of computational complexityMore costly than additions for fixed-point processorsSame cost as additions for floating-point processors, but number of operations is comparableCarnegieMellonSlide 5ECE DepartmentComputational Cost of Discrete-Time FilteringConvolution of an N-point input with an M-point unit sample response ....
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IntroFFT - 18-791 Lecture #17INTRODUCTION TO THE FAST...

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