# Chapter 11.05 Fast Fourier Transform Companion Node Observation Part 1 of 3

###### Informal Development of Fourier Series (CHAPTER 11.05)

Companion Node Observation: Part 1 of 3

###### Topic Description

Through a specific case example, with $N=2^{4}=16$ and graphical representations, this video lecture will explain how to identify the “companion nodes”, how to essentially skip the computations involved with the “companion nodes”, and how to save the “computer memory” during the entire “matrix times vector inner and outer product” process. “Distance” between a pair of companion nodes (corresponding to any $L^{th}$ vector, where $L=1, \, 2, \, ..., \, r-1$; and $N=2^{r}$) is explained. By introducing the notation $W^{P}$, general formulas for computing the pairs of companion nodes (corresponding to any $L^{th}$ level vector) are derived and explained. Example for the case $N=2^{r=4}=16$, and graphical representation form are used to facilitate the explanation of “companion nodes”

###### 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 2 of 3 [YOUTUBE 15:14]

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

###### Complete Resources

Get in one place the following: Development of Fast Fourier Transform