Lecture13-fft

Lecture13-fft - CS 312: Algorithm Analysis Lecture #13:...

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Unformatted text preview: CS 312: Algorithm Analysis Lecture #13: Convolution, Overview of the Fast Fourier This work is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License. Slides by: Eric Ringger, with contributions from Mike Jones, Eric Mercer, Sean Warnick; some figures adapted from Dasgupta et al. Announcements HW #8 due now Questions? Project #3 Early: Wednesday Due: next Friday Review assignments: next Friday Reviews due: the Mon. after that Final proof due: the Wed. after that Objectives Introduce you to the convolution operation. See an algorithm for convolution, inspired by polynomial multiplication Discover how to make a divide and conquer algorithm for polynomial evaluation , namely the Fast Fourier Transform (FFT) Use the FFT and Inverse FFT for a faster solution to convolution Polynomial Multiplication 2 1 2 2 1 2 2 2 ( ) 1 2 3 ( ) 2 4 ( ) ( ) ( ) A x x x a a x a x B x x x b b x b x C x A x B x = + + = + + = + + = + + = Polynomial Multiplication is Convolution 2 1 2 2...
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Lecture13-fft - CS 312: Algorithm Analysis Lecture #13:...

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