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INFORMAL DEVELOPMENT OF FOURIER SERIES (CHAPTER 11.05)

 

Unscrambling the FFT: Determination of W^P: Part 1 of 3

 

By Duc Nguyen



TOPIC DESCRIPTION
 
Unscrambling the Fast Fourier Transform (FFT). Using the specific case example N=2**(r=4)=16, and graphical representation, the unscrambling phase (including the bit-reversing phase) of the FFT process is explained, in order to be able to obtain the original unknown complex numbers Cn in "proper orders". Computer implementation of "unscrambling/bit-reversing phase" of the FFT process is explained. Computer implementation of FFT for computing a pair of "companion nodes" and avoiding complex number operations are also explained.

ALL VIDEOS FOR THIS TOPIC
 

Informal Development of Fast Fourier Transform: Part 1 of 3 [YOUTUBE 09:59]

Informal Development of Fast Fourier Transform: Part 2 of 3 [YOUTUBE 12:39]

Informal Development of Fast Fourier Transform: Part 3 of 3 [YOUTUBE 09:46]

Fast Fourier Transform: Factorized Matrix & Operation Count: Part 1 of 4 [YOUTUBE 14:08]

Fast Fourier Transform: Factorized Matrix & Operation Count: Part 2 of 4 [YOUTUBE 14:48]

Fast Fourier Transform: Factorized Matrix & Operation Count: Part 3 of 4 [YOUTUBE 13:45]

Fast Fourier Transform: Factorized Matrix & Operation Count: Part 4 of 4 [YOUTUBE 11:49]

Fast Fourier Transform: Companion Node Observation: Part 1 of 3 [YOUTUBE 11:22]

Fast Fourier Transform: Companion Node Observation: Part 2 of 3 [YOUTUBE 12:56]

Fast Fourier Transform: Companion Node Observation: Part 3 of 3 [YOUTUBE 09:01]

Fast Fourier Transform: Determination of W^P: Part 1 of 4 [YOUTUBE 13:34]

Fast Fourier Transform: Determination of W^P: Part 2 of 4 [YOUTUBE 09:31]

Fast Fourier Transform: Determination of W^P: Part 3 of 4 [YOUTUBE 07:36]

Fast Fourier Transform: Determination of W^P: Part 4 of 4 [YOUTUBE 09:41]

Fast Fourier Transform: Unscrambling the FFT: Determination of W^P: Part 1 of 3 [YOUTUBE 15:07]

Fast Fourier Transform: Unscrambling the FFT: Determination of W^P: Part 1 of 3 [YOUTUBE 15:14]

Fast Fourier Transform: Unscrambling the FFT: Determination of W^P: Part 1 of 3 [YOUTUBE 14:32]


COMPLETE RESOURCES
  Get in one place the following: a textbook chapter, individual YouTube lecture videos, PowerPoint presentation, Worksheet and Multiple Choice Questions on Informal Development of Fourier Series.

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Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Based on a work at http://mathforcollege.com/nm.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

 

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