Section 1 : Introduction to the Fourier transform

Lecture 1 Course materials (reader, MATLAB code, Python code)
Lecture 2 Nontechnical description of Fourier transform 00:06:34 Duration
Lecture 3 Examples of Fourier transform applications 00:11:48 Duration
Lecture 4 MATLAB, Octave, Python, or just watch 00:02:29 Duration
Lecture 5 INTRODUCTION TO BRAINMEASURES PROCTOR SYSTEM

Section 2 : Foundations of the Fourier transform

Lecture 1 Course materials (reader, MATLAB code, Python code, exercises)
Lecture 2 Complex numbers- 00:13:59 Duration
Lecture 3 xkcd explanation of why we need complex numbers
Lecture 4 Euler's formula e^ik 00:09:31 Duration
Lecture 5 Sine waves and complex sine waves 00:13:56 Duration
Lecture 6 Dot product 00:16:29 Duration
Lecture 7 Complex dot product 00:09:00 Duration

Section 3 : The discrete Fourier transform

Lecture 1 Course materials (reader, MATLAB code, Python code, exercises)
Lecture 2 How the discrete Fourier transform works 00:12:08 Duration
Lecture 3 Converting indices to frequencies 00:08:27 Duration
Lecture 4 About Certification
Lecture 5 INTRODUCTION TO BRAINMEASURES PROCTOR SYSTEM
Lecture 6 Normalized time vector
Lecture 7 Positive and negative frequencies 00:04:47 Duration
Lecture 8 Accurate scaling of Fourier coefficients 00:06:18 Duration
Lecture 9 Interpreting phase values
Lecture 10 Averaging Fourier coefficients 00:08:57 Duration
Lecture 11 The DC (zero frequency) component 00:07:40 Duration
Lecture 12 Amplitude spectrum vs 00:06:47 Duration
Lecture 13 A note about terminology of Fourier features

Section 4 : The discrete inverse Fourier transform

Lecture 1 Course materials (reader, MATLAB code, Python code, exercises)
Lecture 2 How and why it works 00:10:44 Duration
Lecture 3 Inverse Fourier transform for bandstop filtering

Section 5 : The fast Fourier transform

Lecture 1 Course materials (reader, MATLAB code, Python code, exercises)
Lecture 2 How it works, speed tests 00:07:07 Duration
Lecture 3 The fast inverse Fourier transform 00:02:10 Duration
Lecture 4 The perfection of the Fourier transform 00:06:44 Duration
Lecture 5 Using the fft on matrices 00:07:11 Duration

Section 6 : Frequency resolution and zero padding

Lecture 1 Course materials (reader, MATLAB code, Python code, exercises)
Lecture 2 Sampling and frequency resolution 00:16:17 Duration
Lecture 3 Time-domain zero padding
Lecture 4 Frequency-domain zero padding 00:07:35 Duration
Lecture 5 Sampling rate vs 00:09:04 Duration
Lecture 6 About Certification

Section 7 : Aliasing, stationarity, and violations

Lecture 1 Course materials (reader, MATLAB code, Python code, exercises)
Lecture 2 Aliasing 00:09:41 Duration
Lecture 3 Signal stationarity and non-stationarities 00:05:36 Duration
Lecture 4 Effects of non-stationarities on the power spectrum 00:15:56 Duration
Lecture 5 Solution to understanding nonstationary time series 00:12:35 Duration
Lecture 6 Windowing and Welch's method 00:09:44 Duration
Lecture 7 Instantaneous frequency 00:11:34 Duration

Section 8 : 2D Fourier transform

Lecture 1 Course materials (reader, MATLAB code, Python code, exercises)
Lecture 2 How the 2D FFT works 00:11:10 Duration

Section 9 : Applications of the Fourier transform

Lecture 1 Course materials (reader, MATLAB code, Python code, exercises)
Lecture 2 Rhythmicity in walking (gait) 00:06:06 Duration
Lecture 3 Rhythmicity in electrical brain waves 00:07:03 Duration
Lecture 4 Time series convolution 00:02:09 Duration
Lecture 5 Narrowband temporal filtering 00:08:09 Duration
Lecture 6 2D image filtering 00:07:29 Duration
Lecture 7 Image narrowband filtering 00:05:55 Duration
Lecture 8 Real data from trends 00:04:11 Duration