MASTER THE FOURIER TRANSFORM AND ITS APPLICATIONS

In MATLAB and in Python

This project showcases BiophysicsLab’s expertise with the Fourier Transform in both MATLAB and Python. Below are my PDF notes from Dr. Mike X Cohen’s Udemy course.

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TABLE OF CONTENTS – Master the Fourier transform and its applications in MATLAB and Python

Lesson	Description	Page
	Section 1: Introduction to the Fourier transform	2
2	Nontechnical description of Fourier transform	2
3	Examples of Fourier transform applications	3
	Section 2: Foundations of the Fourier transform	16
9	Euler’s formula e^ik	16
10	Sine waves and complex sine waves	21
11	Dot product	25
12	Complex dot product	27
	Section 3: The discrete Fourier transform	31
14	How the discrete Fourier transform works	31
15	Converting indices to frequencies	33
16	Shortcut: converting indices to frequencies	35
17	Normalized time vector	36
18	Positive and negative frequencies	37
19	Accurate scaling of Fourier coefficients	38
20	Interpreting phase values	39
21	Averaging Fourier coefficients	40
22	The DC (zero frequency) component	42
23	Amplitude spectrum vs. power spectrum	43
24	A note about terminology of Fourier features	45
	Section 4: The discrete inverse Fourier transform	46
26	How and why it works	46
27	Inverse Fourier transform for bandstop filtering	48
	Section 5: The fast Fourier transform	49
29	How it works, speed tests	49
30	The fast inverse Fourier transform	51
31	The perfection of the Fourier transform	52
32	Using the fft on matrices	55
	Section 6: Frequency resolution and zero padding	56
34	Sampling and frequency resolution	56
35	Time-domain zero padding	59
36	Frequency-domain zero padding	61
37	Sampling rate vs. signal length	63
38	Course tangent: self-accountability in online learning	64
	Section 7: Aliasing, stationarity, and violations	64
40	Aliasing	65
41	Signal stationarity and non-stationarities	69
42	Effects of non-stationarities on the power spectrum	71
43	Solution to understanding nonstationary time series	76
44	Windowing and Welch’s method	80
45	Instantaneous frequency	81
	Section 8: 2D Fourier transform	82
46	How the 2D FFT works	82
	Section 9: Applications of the Fourier transform	88
47	Rhythmicity in walking (gait)	88
48	Rhythmicity in electrical brain waves	89
49	Time series convolution	89
50	Narrowband temporal filtering	91
51	2D image filtering	93
52	Image narrowband filtering	94
53	Real data from trends.google.com!	95
	Notes	98
	FFT Examples	98
	Amplitude Spectrum	99
	Power Spectrum	99
	Power Spectrum in Decibels	99
	Inverse FFT	99
	Sinc function and Whittaker-Shannon interpolation formula	100
	MATLAB commands	100
	Utility code	101
	References	104

Purchase Details

While some MATLAB code is included in these notes, the full MATLAB and Python code for MASTER THE FOURIER TRANSFORM AND ITS APPLICATIONS are omitted. The code (for both MATLAB and Python) are included as part of Dr. Mike X Cohen’s Udemy class, as listed in the notes.

However, BiophysicsLab offers consulting services to explore individual lessons from these notes. For example, see my post on this website exploring lesson 43 – Solutions to understanding nonstationary time series: Short-time Fourier Transform

Master the Fourier Transform and Its Applications Using MATLAB – Open PDF 42 downloads 10.1 MB

$5.00