#### Section 1 : Introduction to the Fourier transform

 Lecture 1 Course materials (reader, MATLAB code, Python code) Text Lecture 2 Nontechnical description of Fourier transform 6:34 Lecture 3 Examples of Fourier transform applications 11:48 Lecture 4 MATLAB, Octave, Python, or just watch 2:29 Lecture 5 INTRODUCTION TO BRAINMEASURES PROCTOR SYSTEM Pdf

#### Section 2 : Foundations of the Fourier transform

 Lecture 6 Course materials (reader, MATLAB code, Python code, exercises) Text Lecture 7 Complex numbers- 13:59 Lecture 8 xkcd explanation of why we need complex numbers Text Lecture 9 Euler's formula e^ik 9:31 Lecture 10 Sine waves and complex sine waves 13:56 Lecture 11 Dot product 16:29 Lecture 12 Complex dot product 9:0

#### Section 3 : The discrete Fourier transform

 Lecture 13 Course materials (reader, MATLAB code, Python code, exercises) Text Lecture 14 How the discrete Fourier transform works 12:8 Lecture 15 Converting indices to frequencies 8:27 Lecture 16 About Certification Pdf Lecture 17 INTRODUCTION TO BRAINMEASURES PROCTOR SYSTEM Pdf Lecture 18 Normalized time vector Lecture 19 Positive and negative frequencies 4:47 Lecture 20 Accurate scaling of Fourier coefficients 6:18 Lecture 21 Interpreting phase values Lecture 22 Averaging Fourier coefficients 8:57 Lecture 23 The DC (zero frequency) component 7:40 Lecture 24 Amplitude spectrum vs 6:47 Lecture 25 A note about terminology of Fourier features

#### Section 4 : The discrete inverse Fourier transform

 Lecture 26 Course materials (reader, MATLAB code, Python code, exercises) Text Lecture 27 How and why it works 10:44 Lecture 28 Inverse Fourier transform for bandstop filtering

#### Section 5 : The fast Fourier transform

 Lecture 29 Course materials (reader, MATLAB code, Python code, exercises) Text Lecture 30 How it works, speed tests 7:7 Lecture 31 The fast inverse Fourier transform 2:10 Lecture 32 The perfection of the Fourier transform 6:44 Lecture 33 Using the fft on matrices 7:11

#### Section 6 : Frequency resolution and zero padding

 Lecture 34 Course materials (reader, MATLAB code, Python code, exercises) Text Lecture 35 Sampling and frequency resolution 16:17 Lecture 36 Time-domain zero padding Lecture 37 Frequency-domain zero padding 7:35 Lecture 38 Sampling rate vs 9:4 Lecture 39 About Certification Pdf

#### Section 7 : Aliasing, stationarity, and violations

 Lecture 40 Course materials (reader, MATLAB code, Python code, exercises) Text Lecture 41 Aliasing 9:41 Lecture 42 Signal stationarity and non-stationarities 5:36 Lecture 43 Effects of non-stationarities on the power spectrum 15:56 Lecture 44 Solution to understanding nonstationary time series 12:35 Lecture 45 Windowing and Welch's method 9:44 Lecture 46 Instantaneous frequency 11:34

#### Section 8 : 2D Fourier transform

 Lecture 47 Course materials (reader, MATLAB code, Python code, exercises) Text Lecture 48 How the 2D FFT works 11:10

#### Section 9 : Applications of the Fourier transform

 Lecture 49 Course materials (reader, MATLAB code, Python code, exercises) Text Lecture 50 Rhythmicity in walking (gait) 6:6 Lecture 51 Rhythmicity in electrical brain waves 7:3 Lecture 52 Time series convolution 2:9 Lecture 53 Narrowband temporal filtering 8:9 Lecture 54 2D image filtering 7:29 Lecture 55 Image narrowband filtering 5:55 Lecture 56 Real data from trends 4:11