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Fast Fourier Transform

In this video we show how the Discrete Fourier Transform operation can be written as a matrix operation. While this is convenient, in its native form, this is a computationally expensive operation. However, we show how the Cooley-Tukey algorithm can be used to decompose this matrix operation into a series of smaller matrix operations, thereby making it a computationally efficient and fast algorithm. This algorithm is known as the Fast Fourier Transform (FFT) and is considered to be one of the most important numerical algorithms in history. In addition the outlining the mathematical theory behind the FFT, we look at how this can be leveraged in Matlab and show a concrete example of the FFT applied to an audio frequency analysis problem. Cooley, James W. and Tukey, John W., "An Algorithm for the Machine Calculation of Complex Fourier Series," Mathematics of Computation, Vol. 19, April 1965, pages 297-301. Topics and timestamps: 0:00 – Introduction 3:42 – DFT in matrix form 11:57 – The FFT algorithm 30:08 – Validate matrix decomposition 41:01 – Example of FFT on audio data Lecture notes and code can be downloaded from https://github.com/clum/YouTube/tree/... All Fourier analysis videos in a single playlist (   • Fourier Analysis  ) #FourierAnalysis #FourierSeries All Matlab/Simulink videos in a single playlist (   • Working with Matlab  ) #Matlab #Simulink You can support this channel via Patreon at   / christopherwlum   or by clicking on the ‘Thanks’ button underneath the video. Thank you for your help!