# Chapter 11.05 Informal Development of Fourier Series Part 3 of 3

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

Informal Development of Fast Fourier Transform: Part 3 of 3

###### Topic Description

Any given periodic function $f$ can be expressed in terms of the unknown, complex numbers $\tilde{C}_n$, where the unknown complex numbers $\tilde{C}_n$ can be computed by the double summations over the indexes $n$, and $k$. This formulation will lead to expensive “matrix times vector” operations. It can be demonstrated that computation of the unknown complex numbers $\tilde{C}_n$ will require “matrix times vector” operations, that will involve with 16 complex multiplications, and 12 complex additions, corresponding to the index $n=1,\, 2,\, ....,\,N-1=3$; with $N=4$ data points. Using the definition of the complex number $W=e^{-i \frac{2\pi}{N}}$ with $\pi=3.1416$ and together with Euler identity, this video lecture will explain the important property of $W$, such as $W^{nk}=W^{p}$, where $p=\mod(nk,N)$.

###### 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