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]

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