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