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How the Fourier Transform Works
Introduction to the Course
What is the Fourier Transform? (2:58)
Who was Fourier?
Fourier's Early Life (3:59)
Fourier and the French Revolution (3:52)
Heat Transfer and the Fourier Series (4:00)
Sine Waves
What is a Sinusoid? (5:09)
Adding Sines and Cosines (5:56)
Degrees and Radians (8:29)
How Sines and Cosines are Calculated (10:00)
Worksheet (10:10)
Complex Numbers
Euler's Number (6:06)
The History of Complex Numbers (10:32)
What is an Imaginary Number? (6:13)
The Complex Exponential (7:13)
The 3 forms of a Complex Number (3:41)
Complex Arithmetic Part 1 (7:34)
Complex Arithmetic Part 2 (7:13)
Worksheet (10:41)
Convolution
What is Convolution? (7:20)
An important property of Convolution (7:17)
A Convolution Shortcut (5:04)
Worksheet (5:52)
The Fourier Series
The Fourier Series Equation (12:44)
Negative Frequency and Real Signals (13:39)
Calculating the Fourier Series (5:53)
Making sense of the results (7:52)
The problem with the Fourier Series (6:03)
Worksheet
The Fourier Transform
The Infinities of the Fourier Transform (8:27)
Continuous Frequency (7:39)
Calculating the Fourier Transform (6:38)
Worksheet
The Problem with the Fourier Transform (5:55)
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How Sines and Cosines are Calculated
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