Section 1 : Introduction to the Fourier transform
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Lecture 1 | Course materials (reader, MATLAB code, Python code) | |
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Lecture 2 | Nontechnical description of Fourier transform | 00:06:34 Duration |
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Lecture 3 | Examples of Fourier transform applications | 00:11:48 Duration |
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Lecture 4 | MATLAB, Octave, Python, or just watch | 00:02:29 Duration |
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Lecture 5 | INTRODUCTION TO BRAINMEASURES PROCTOR SYSTEM |
Section 2 : Foundations of the Fourier transform
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Lecture 1 | Course materials (reader, MATLAB code, Python code, exercises) | |
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Lecture 2 | Complex numbers- | 00:13:59 Duration |
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Lecture 3 | xkcd explanation of why we need complex numbers | |
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Lecture 4 | Euler's formula e^ik | 00:09:31 Duration |
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Lecture 5 | Sine waves and complex sine waves | 00:13:56 Duration |
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Lecture 6 | Dot product | 00:16:29 Duration |
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Lecture 7 | Complex dot product | 00:09:00 Duration |
Section 3 : The discrete Fourier transform
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Lecture 1 | Course materials (reader, MATLAB code, Python code, exercises) | |
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Lecture 2 | How the discrete Fourier transform works | 00:12:08 Duration |
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Lecture 3 | Converting indices to frequencies | 00:08:27 Duration |
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Lecture 4 | About Certification | |
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Lecture 5 | INTRODUCTION TO BRAINMEASURES PROCTOR SYSTEM | |
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Lecture 6 | Normalized time vector | |
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Lecture 7 | Positive and negative frequencies | 00:04:47 Duration |
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Lecture 8 | Accurate scaling of Fourier coefficients | 00:06:18 Duration |
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Lecture 9 | Interpreting phase values | |
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Lecture 10 | Averaging Fourier coefficients | 00:08:57 Duration |
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Lecture 11 | The DC (zero frequency) component | 00:07:40 Duration |
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Lecture 12 | Amplitude spectrum vs | 00:06:47 Duration |
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Lecture 13 | A note about terminology of Fourier features |
Section 4 : The discrete inverse Fourier transform
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Lecture 1 | Course materials (reader, MATLAB code, Python code, exercises) | |
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Lecture 2 | How and why it works | 00:10:44 Duration |
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Lecture 3 | Inverse Fourier transform for bandstop filtering |
Section 5 : The fast Fourier transform
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Lecture 1 | Course materials (reader, MATLAB code, Python code, exercises) | |
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Lecture 2 | How it works, speed tests | 00:07:07 Duration |
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Lecture 3 | The fast inverse Fourier transform | 00:02:10 Duration |
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Lecture 4 | The perfection of the Fourier transform | 00:06:44 Duration |
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Lecture 5 | Using the fft on matrices | 00:07:11 Duration |
Section 6 : Frequency resolution and zero padding
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Lecture 1 | Course materials (reader, MATLAB code, Python code, exercises) | |
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Lecture 2 | Sampling and frequency resolution | 00:16:17 Duration |
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Lecture 3 | Time-domain zero padding | |
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Lecture 4 | Frequency-domain zero padding | 00:07:35 Duration |
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Lecture 5 | Sampling rate vs | 00:09:04 Duration |
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Lecture 6 | About Certification |
Section 7 : Aliasing, stationarity, and violations
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Lecture 1 | Course materials (reader, MATLAB code, Python code, exercises) | |
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Lecture 2 | Aliasing | 00:09:41 Duration |
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Lecture 3 | Signal stationarity and non-stationarities | 00:05:36 Duration |
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Lecture 4 | Effects of non-stationarities on the power spectrum | 00:15:56 Duration |
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Lecture 5 | Solution to understanding nonstationary time series | 00:12:35 Duration |
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Lecture 6 | Windowing and Welch's method | 00:09:44 Duration |
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Lecture 7 | Instantaneous frequency | 00:11:34 Duration |
Section 8 : 2D Fourier transform
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Lecture 1 | Course materials (reader, MATLAB code, Python code, exercises) | |
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Lecture 2 | How the 2D FFT works | 00:11:10 Duration |
Section 9 : Applications of the Fourier transform
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Lecture 1 | Course materials (reader, MATLAB code, Python code, exercises) | |
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Lecture 2 | Rhythmicity in walking (gait) | 00:06:06 Duration |
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Lecture 3 | Rhythmicity in electrical brain waves | 00:07:03 Duration |
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Lecture 4 | Time series convolution | 00:02:09 Duration |
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Lecture 5 | Narrowband temporal filtering | 00:08:09 Duration |
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Lecture 6 | 2D image filtering | 00:07:29 Duration |
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Lecture 7 | Image narrowband filtering | 00:05:55 Duration |
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Lecture 8 | Real data from trends | 00:04:11 Duration |