mws_gen_fft_spe_pptfastfourierdevl

mws_gen_fft_spe_pptfastfourierdevl - Numerical Methods Fast...

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Unformatted text preview: Numerical Methods Fast Fourier Transform Part: Informal Development of Fast Fourier Transform http://numericalmethods.eng.usf.edu For more details on this topic Go to http://numericalmethods.eng.usf.edu Click on Keyword Click on Fast Fourier Transform You are free to Share – to copy, distribute, display and perform the work to Remix – to make derivative works Under the following conditions Attribution — You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). Noncommercial — You may not use this work for commercial purposes. Share Alike — If you alter, transform, or build upon this work, you may distribute the resulting work only under the same or similar license to this one. Chapter 11.05: Informal Development of Fast Fourier Transform Major: All Engineering Majors Authors: Duc Nguyen http://numericalmethods.eng.usf.edu Numerical Methods for STEM undergraduates http://numericalmethods.eng.usf.edu 11/01/11 5 Lecture # 11 Informal Development of Fast Fourier Transform Recall the DFT pairs of Equations (20) and (21) of Chapter 11.04 and swapping the indexes , one obtains n k ∑- = =- = 1 2 ) ( ~ N k k N w in n e k f C π ∑- = = = 1 2 ~ 1 ) ( N n k N w in n e C N k f π (1) (2) where 1 ,..., 3 , 2 , 1 , ,- = N k n (3) N i e W π 2- = ( 29 1 2 = =- π i N e W hence Let (4) 6 http://numericalmethods.eng.usf.edu Informal Development cont. Then Eq. (1) and Eq. (2) become ∑- = = = 1 ) ( ) ( ~ ~ N k nk n W k f n C C ∑- =- = 1 ~ 1 ) ( N n nk n W C N k f (5) Assuming , then ) 2 ( 2 4 = = = r N = --------- ) 3 ( ) 2 ( ) 1 ( ) ( ) 3 ( ~ ) 2 ( ~ ) 1 ( ~ ) ( ~ 1 1 1 1 1 1 1 1 9 6 3 6 4 2 3 2 1 f f f f C C C C W W W W W W W W W N (5A) 7 http://numericalmethods.eng.usf.edu Informal Development cont....
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mws_gen_fft_spe_pptfastfourierdevl - Numerical Methods Fast...

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