Negative Frequency, Imaginary Numbers and the Complex Conjugate

What is negative frequency? Why do we need it? What have imaginary numbers got to do with it? Is it a physical phenomenon or just a quirk of the maths?

In this video, we look at what makes a signal real and why negative frequencies make them so. We also look at the role the Inverse Fourier Transform plays in the process, and I demonstrate a physical effect of negative frequency in the real world, just in case you thought that negative frequency was only a quirk of the maths.

Book: How the Fourier Series Works
https://www.amazon.com/dp/B0B1BY5H6T

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Playlist: Understand the output of the FFT
https://www.youtube.com/playlist?list=PLWMUMyAolbNv9c9qMoksBWv_YDn57EJHz

Image of Sound Level Meter used in Thumbnail by Jin Zan:
https://commons.wikimedia.org/wiki/File:Sound_level_meter,_DVM85.jpg
Licensed under the Creative Commons Attribution-Share Alike 4.0 International license
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0:00 - Introduction
1:08 - Ident
1:12 - What is a real signal?
2:12 - The Fourier Transform
3:36 - A way to understand what negative frequency is
5:11 - Why the sine component is reversed
6:22 - The frequency domain and complex numbers
7:04 - The Fourier Cube and the Inverse Fourier Transform
10:22 - Negative frequency and the complex conjugate
11:27 - A real-world example of the effects of negative frequency
14:46 - Review and conclusion
15:37 - End Screen